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If the water depth is 2 m. Angular velocity. New York: Find the gauge pressure at the base of the tank when the mercury deflection in the open limb of the V-tube is i mm above. If the gauge balances a total mass of 10 kg placed on the piston. The remaining space is filled with air under pressure. Calculate the pressure intensity at the bottom of the tank holding 5 m of the solution.

RecommeruJed reading 1. Editors Handbook of applied hydraulics. Take the ratio. The upper end of the cylinder is connected to a gas supply under pressure. A manometer consists of a glass tube. Explain what will happen if the storage increases beyond 4 m. If the water stands to depth of 5 m and 3 m on either side.

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A radial gate. A storage tank of a sewage treatment plant is to discharge excess sewage into the sea through a horizontal rectangular culvert 1 m deep and 1. In order to measure the pressure difference between two points in a pipeline carrying water. When the sea water stands to the hinge level.

A dock gate is to be reinforced with three identical horizontal beams. Determine i the total hydrostatic thrust and its location on the gate when the storage depth is 4 m. The profile of the inner face of a dam is a parabola with equation y the base.

If d and h are the diameter and height of the cylinder respectively. The dam retains water to a depth of 30 m above Determine the hydrostatic thrust on the dam per unit length.

A homogeneous wooden cylinder of circular section. A sector gate of radius 3 m and length 4 m retains water as shown in fig. If the relative density of the material of the buoy is s. A conical buoy floating in water with its apex downwards has a diameter d and a vertical height h. Platform Figure 2. If the buoy is anchored with a chain attached to the centre of its base. Single beam b. A platform constructed by joining two 10 m long wooden beams as shown in fig.

Examine the stability of a single beam and of the platform and determine their stability moments. Parabolic profile of the inner face of a dam A floating platform for offshore drilling purposes is in the form of a square floor supported by 4 vertical cylinders at the corners. Determine the location of the centroid of the assembly in terms of the side L of the floor and the depth of submergence h of the cylinders.

Prove that it is unstable. The water surface in each compartment is free to move. The barge has two compartments each 4 m wide and 20 m long. An open rectangular tank 4 m long and 3 m wide contains water up to a depth of 2 m. A U-tube acceleration meter consists of two vertical limbs connected by a horizontal tube of mm long parallel to the direction of motion.

Prove that. Hence calculate the thrust of the liquid on the top of a closed vertical cylinder of mm diameter.

Civil Engineering Hydraulics 3rd Edition

A rectangular barge 10 m wide and 20 m long is 5 m deep and weighs 6 MN when loaded without any ballast. Pathline Figure 3. Due to the diffusivity phenomena of fluids and their flows. Nalluri 3. More appropriate for describing the fluid motion is to know the flow characteristics such as velocity and pressure. Velocity vector Descriptions of fluid flow In any flow field.

The coordinates of a particle A x. In the Lagrangian method of describing the fluid motion one is concerned to trace the paths of the individual fluid particles elements and to find their velocities. Chapter 3 Fluid Flow Concepts and Measurements c.

A continuous curve traced tangentially to the velocity vector at each point in the flow field is known as the streamline.. For example. In steady flow. A particle always moves tangentially to the streamline and hence in steady flow the path of a particle is a streamline.

The velocity vector at a point in the flow field is a sand t and can be resolved into u. Mathematically this can be expressed as: In two dimensional flow. Flow through a pipe may usually be characterised as one dimensional.

Considering an elemental stream tube of the flow fig. Since the velocity at any point along a streamline is tangential to it. This concept of the streamtube is very useful in deriving the continuity equation. Three dimensional flow is the most general type of flow in which the velocity vector varies with space and is generally complex.

Flow through a diverging pipe at a constant rate is steady non-uniform flow and at a varying rate is unsteady non-uniform flow. The non-uniform velocity distribution of real fluids close to a boundary causes particles to deform with a small degree of rotation whereas.

Thus in terms of the velocity vector V s. For incompressible steady flow. Velocity vectors a. Fluid flows between straight parallel boundaries fig. The total normal acceleration can now be written as: Examples of streamline patterns and their corresponding types of acceleration in steady flows: The vector change L1 can be resolved into two V V components. Curved path Figure 3. In laminar flow. The type of a flow is identified by the Reynolds number.

Tangential convective accelerations c. Viscous shear stresses dominate in this kind of flow in which the shear stress and velocity distribution are governed by Newton's law of viscosity equation 1. These turbulent fluctuations cause an exchange of momentum setting up additional shear stresses of large magnitudes.

In turbulent flows.. Tangential and normal convective accelerations Streamline patterns and types of acceleration Flow in a concentric curved bend fig. No accelerations exist b. Normal convective accelerations Figure The coefficient n.

An equation of the form similar to Newton's law of viscosity equation 1. Reynolds number represents the ratio of inertial forces to the viscous forces that exist in the flow field and is dimensionless. The study of ideal fluid motion is a valuable background information to encounter the problems of civil engineering hydraulics. Water has a relatively low viscosity and is practically incompressible and is found to behave like an ideal fluid.

A fluid in motion experiences. The presence of such a complex system of forces in real fluid flow problems makes the analysis very complicated. The flow through a pipe is always laminar if the corresponding Reynolds number R.

Bernoulli's theorem states that the total energy at all points along a steady continuous streamline of an ideal incompressible fluid flow is constant and is written as: For this reason equation 3. On integration along the streamline. All frictional forces are assumed to be zero and the flow is irrotational i. The first term. The second term. For a steady flow situation between two sections of a flow field. Note a A general energy equation from the principles of conservation of energy can be derived for a fluid flow taking into account the mass.

The units of the total energy can be written as N mIN of fluid or metres of fluid in which case it is known as total head. The turbulent losses also depend upon the roughness of the interior surface of the pipe wall and the fluid properties of density and viscosity.

The frictional losses depend upon the type of flow. Thus the Bernoulli's equation is a specific case of energy equation. I is the internal energy. The third term. In the case of uniform velocity distribution fig. Uniform distribution Figure 3. In the case of non-uniform velocity distribution fig.

V being the average velocity at the section. This phenomenon is known as separation and greatly reduces the efficiency of the system. At any point. Rising main of uniform diameter Figure 3. Horizontal converging-diverging pipe Separation and cavitation phenomena.

The whole phenomenon is called cavitation and should be avoided while designing any hydraulic system. Low Pressure region Liberation of air bubbles z z. With further liberation of gases the bubbles tend to grow in size eventually blocking the pipe section thus allowing the discharge to take place intermittently. If the tiny air bubbles formed at the separation point are carried to a high pressure region fig. As the elevation z increases. P is commonly referred to as the Boussinesq coefficient.

In these regions of separation turbulent eddies form with a consequence of pressure loss dissipating in the form of heat energy. F dt is called the impulse of applied force F. MLT-I and Newton's second law of motion states that the resultant external force acting on any body in any direction is equal to the rate of change of momentum of the body in that direction.

In x direction.

AI is experimentally found to be the same as the pressure PI. Sudden contraction Figure Equation iv reduces to: The head or energy loss between 1 and 2 from equations i. Sudden expansion b. By continuity. Venturi meter Figure 3.

Bernoulli's equation between inlet section and constriction: The actual discharge is. Orifice meter a. Orifice b. V2 pg 2g Continuity equation gives: The gradual transitions of the venturi meter fig. The transition in the case of an orifice plate meter fig. The reduction in the constriction diameter causes velocity to increase.

High velocities at the constriction cause low pressures in the system and if these fall below the vapour pressure limit of the fluid. Its discharge coefficient has a much lower value 0. This ratio may be kept between t and and a more common value IS 2'. The stagnation pressure at point 2 velocity is zero.

V2gh where C. Sharp edged orifice C.

Borda's re-entrant mouthpieces C. Mouthpiece b. Divergent tube Figure 3.

Total discharge through the entire opening. Bell mouthed orifice L. The actual discharge through the strip area. The discharge through a submerged orifice Discharge through the strip. ModijicaJion of eqlUJlion 3. Discharge under varying head: Since the head causing ftow is varying.

We can write: Orifice in inclined wall large rectangular orifice c. Time taken to lower the water level from HI to H2: Submerged orifice Velocity of approach - If h is the head at any instant t see fig.

Orifice with approach velocity Figure 3. In general. A weir or a notch may be regarded as a special form of large orifice with the free water surface below its upper edge.

The total discharge. The head over the sill of such an obstruction is related to the discharge through energy principles. Thus equation 3. V2g b f: The discharge over such a weir may be computed by using the formula for a suppressed no end contractions rectangular weir with equal sill width.

This is known as Francis formula. The discharge. A discharge equation similar to that of the weir. The profile of an Ogee spillway conforms to the shape of a sharp crested weir see fig. H Figure 3. He being any other energy head with a corresponding discharge coefficient. Va being the velocity of approach. When the downstream water level is above the sill level. HI H2 mJO' 3. If the. Effect of submergence of flow measuring structures If the water level H2 downstream of a measuring device is below the sill level.

Qf and the above equations are valid to compute the free flows. The non-modular flow. Example 3. Determine the pressure intensity at the entrance to the turbine. Average velocities. Figure 3. Assuming no losses between 2 and 3. The pressure difference between the normal and constricted sections of the pipe is measured by an inverted V-tube.

Determine i the difference in pressure between these two sections when the discharge through the system is lis. By the continuity equation: Compute the discharge in lis through the pipe if its length is 20 m.

Solution Manual to Hydraulics in Civil and Environmental Engineering (4th edition)

The free water surface in the sump is 2 m above the centre of the inlet and the pipe is laid at a slope of 1 vertical: Neglect air resistance. In the horizontal direction. If the jet under a particular flow condition strikes the ground at a horizontal distance of 15 m from the nozzle.

Consider the three points. Take atmospheric pressure as 1 bar and neglect all losses. In the vertical direction. Band C along the siphon system as shown in fig. P2 pg.

In x-direction: VI and in y-direction: Let F" and Fy be the two components of the total force. Gravity forces are zero along the horizontal plane and the only forces acting on the fluid mass are pressure and momentum forces. If a 10 mm diameter horizontal jet of water impinging 50 mm below the hinge keeps the plate inclined at 30" to the vertical.

Resultant force on the bend. A mm x mm square metal plate. According to Newton's third law of motion. Inclined plate Figure 3. Hinged plate Taking moments about the hinge. Case of sudden expansion: Bernoulli's equation between inlet and throat: The throat diameter of the meter is mm and the pressure at the throat is mm of mercury below atmosphere.

Flow rate. The centre line velocity in the pipe. The stagnation pressure at the centre line of the pipe is mm of water more than the static pressure Determine the rate of flow in lIs. From equation 3' When the flow of water into the tank was shut off. Equation 3. A right angled triangular notch is used for gauging the flow of a laboratory flume. J v3dy and J v2dy will give V. The spillway is spanned by piers to support a bridge deck above. The flow between the piers and abutments is contracted.

The kinetic energy correction factor a. Determine the number of spans required in order to pass the flood discharge with the head not exceeding 2 m. Each pier has two end contractions and abutment one. The momentum correction factor. If the mean velocity of flow is V. The clear span between piers is limited to 6 m. British Standards Institution. If the velocity of approach. BS From the discharge equation we can now compute the corresponding head for this flow.

A stage head -discharge relationship can be established by using appropriate discharge coefficients read from fig. Recommended reading 1. The radius of this bucket is 5 m and when the spillway is discharging 5 cumecs of water per metre length of crest. Hence provide five piers.

The spillway section of a dam ends in a curved shape known as the bucket deflecting water away from the dam. Determine the magnitude of the convective acceleration at the beginning and end of this length. Compare the resulting normal or centripetal acceleration with the acceleration due to gravity. In fact the spillway is capable of discharging a larger flood flow at the specified design head of 2 m. Part I Methods for the measurement offluidflow in pipes. Part 4A Methods of measurement of liquid flow in open channels.

Hence find the angle of inclination with which the jet issues from the nozzle. R is pipe radius. Show that the kinetic energy correction factor for this flow is 2. The smaller section is 4 m below the other and if the discharge is lis determine the energy loss and the direction of flow. Water is pumped from a sump see fig. A Pitot tube placed in front of a submarine moving horizontally in sea 16 m below the water surface.

Calculate the resultant thrust the fluid exerts on the floor. If the ends of the bend are anchored by tie-rods at right angles to the pipeline. Find the smallest diameter of the throat to ensure that the pressure head does not become negative. Neglecting friction. The depth upstream of the sluice gate is 7 m.

Determine the force exerted by the water on the sluice gate assuming uniform velocity distribution in the channel and neglecting frictional losses. Find the magnitude and direction of the force exerted by the oil on the bend. A sluice gate is used to control the flow of water in a horizontal rectangular channel. The diameter of pipe bend is mm at inlet and mm at outlet and the flow is turned through " in a vertical plane. The pressure at the inlet to the bend is 2 m of oil.

This includes loss of drinking water treatment and water supply, which may result in loss of drinking water or severe water contamination. It may also cause the loss of sewage disposal facilities. Lack of clean water combined with human sewage in the flood waters raises the risk of waterborne diseases , which can include typhoid , giardia , cryptosporidium , cholera and many other diseases depending upon the location of the flood.

Damage to roads and transport infrastructure may make it difficult to mobilize aid to those affected or to provide emergency health treatment. Flood waters typically inundate farm land, making the land unworkable and preventing crops from being planted or harvested, which can lead to shortages of food both for humans and farm animals. Entire harvests for a country can be lost in extreme flood circumstances. Some tree species may not survive prolonged flooding of their root systems.

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The impact on those affected may cause psychological damage to those affected, in particular where deaths, serious injuries and loss of property occur. Urban flooding can cause chronically wet houses, leading to the growth of indoor mold and resulting in adverse health effects, particularly respiratory symptoms. In the United States , industry experts estimate that wet basements can lower property values by 10—25 percent and are cited among the top reasons for not downloading a home.

Federal Emergency Management Agency FEMA , almost 40 percent of small businesses never reopen their doors following a flooding disaster.

Flood waters provide much needed water resources in arid and semi-arid regions where precipitation can be very unevenly distributed throughout the year and kills pests in the farming land. Freshwater floods particularly play an important role in maintaining ecosystems in river corridors and are a key factor in maintaining floodplain biodiversity.

For some fish species, an inundated floodplain may form a highly suitable location for spawning with few predators and enhanced levels of nutrients or food. Bird populations may also profit from the boost in food production caused by flooding.

The viability of hydropower , a renewable source of energy, is also higher in flood prone regions. Flood safety planning Aftermath of flooding in Colorado, In the United States, the National Weather Service gives out the advice Turn Around, Don't Drown" for floods; that is, it recommends that people get out of the area of a flood, rather than trying to cross it.

At the most basic level, the best defense against floods is to seek higher ground for high-value uses while balancing the foreseeable risks with the benefits of occupying flood hazard zones. Structures, such as bridges, that must unavoidably be in flood hazard areas should be designed to withstand flooding.

Areas most at risk for flooding could be put to valuable uses that could be abandoned temporarily as people retreat to safer areas when a flood is imminent. Planning for flood safety involves many aspects of analysis and engineering, including: observation of previous and present flood heights and inundated areas, statistical, hydrologic , and hydraulic model analyses, mapping inundated areas and flood heights for future flood scenarios, long-term land use planning and regulation, engineering design and construction of structures to control or withstand flooding, intermediate-term monitoring, forecasting , and emergency-response planning, and short-term monitoring, warning , and response operations.

Each topic presents distinct yet related questions with varying scope and scale in time, space, and the people involved. Attempts to understand and manage the mechanisms at work in floodplains have been made for at least six millennia. Defenses such as detention basins , levees , [28] bunds , reservoirs , and weirs are used to prevent waterways from overflowing their banks.

When these defenses fail, emergency measures such as sandbags or portable inflatable tubes are often used to try to stem flooding. Coastal flooding has been addressed in portions of Europe and the Americas with coastal defenses , such as sea walls , beach nourishment , and barrier islands.

In the riparian zone near rivers and streams, erosion control measures can be taken to try to slow down or reverse the natural forces that cause many waterways to meander over long periods of time. Flood controls, such as dams, can be built and maintained over time to try to reduce the occurrence and severity of floods as well.

In the United States, the U. Army Corps of Engineers maintains a network of such flood control dams. In areas prone to urban flooding, one solution is the repair and expansion of man-made sewer systems and stormwater infrastructure.

Another strategy is to reduce impervious surfaces in streets, parking lots and buildings through natural drainage channels, porous paving , and wetlands collectively known as green infrastructure or sustainable urban drainage systems SUDS. Areas identified as flood-prone can be converted into parks and playgrounds that can tolerate occasional flooding. Ordinances can be adopted to require developers to retain stormwater on site and require buildings to be elevated, protected by floodwalls and levees , or designed to withstand temporary inundation.

Property owners can also invest in solutions themselves, such as re-landscaping their property to take the flow of water away from their building and installing rain barrels , sump pumps , and check valves. Analysis of flood information A series of annual maximum flow rates in a stream reach can be analyzed statistically to estimate the year flood and floods of other recurrence intervals there.

Similar estimates from many sites in a hydrologically similar region can be related to measurable characteristics of each drainage basin to allow indirect estimation of flood recurrence intervals for stream reaches without sufficient data for direct analysis. Physical process models of channel reaches are generally well understood and will calculate the depth and area of inundation for given channel conditions and a specified flow rate, such as for use in floodplain mapping and flood insurance.

Conversely, given the observed inundation area of a recent flood and the channel conditions, a model can calculate the flow rate.

Applied to various potential channel configurations and flow rates, a reach model can contribute to selecting an optimum design for a modified channel.

Various reach models are available as of , either 1D models flood levels measured in the channel or 2D models variable flood depths measured across the extent of a floodplain. Physical process models of complete drainage basins are even more complex.

Although many processes are well understood at a point or for a small area, others are poorly understood at all scales, and process interactions under normal or extreme climatic conditions may be unknown. Basin models typically combine land-surface process components to estimate how much rainfall or snowmelt reaches a channel with a series of reach models. For example, a basin model can calculate the runoff hydrograph that might result from a year storm, although the recurrence interval of a storm is rarely equal to that of the associated flood.

Basin models are commonly used in flood forecasting and warning, as well as in analysis of the effects of land use change and climate change.

Flood forecasting Main articles: Flood forecasting and flood warning Anticipating floods before they occur allows for precautions to be taken and people to be warned [31] so that they can be prepared in advance for flooding conditions. For example, farmers can remove animals from low-lying areas and utility services can put in place emergency provisions to re-route services if needed. Emergency services can also make provisions to have enough resources available ahead of time to respond to emergencies as they occur.

People can evacuate areas to be flooded. In order to make the most accurate flood forecasts for waterways , it is best to have a long time-series of historical data that relates stream flows to measured past rainfall events.

Radar estimates of rainfall and general weather forecasting techniques are also important components of good flood forecasting. In areas where good quality data is available, the intensity and height of a flood can be predicted with fairly good accuracy and plenty of lead time.

The output of a flood forecast is typically a maximum expected water level and the likely time of its arrival at key locations along a waterway, [33] and it also may allow for the computation of the likely statistical return period of a flood. According to the U. Many NWS RFCs routinely issue Flash Flood Guidance and Headwater Guidance, which indicate the general amount of rainfall that would need to fall in a short period of time in order to cause flash flooding or flooding on larger water basins.

Users anywhere in the world can use GFMS to determine when floods may occur in their area. Users can view statistics for rainfall, streamflow, water depth, and flooding every 3 hours, at each 12 kilometer gridpoint on a global map. Forecasts for these parameters are 5 days into the future.The upper end of the cylinder is connected to a gas supply under pressure.

The wedge force. Since the body is in static equilibrium. Example 2. Find the speed of the submarine for a manometer deflection of mm. Prove that it is unstable. In areas where good quality data is available, the intensity and height of a flood can be predicted with fairly good accuracy and plenty of lead time. Band C along the siphon system as shown in fig. If this tank of water is lowered with an acceleration equal to that of gravity.