Questions and Answers of Introduction To Fluid Mechanics

Water flows in a rectangular channel at a depth of $750 \mathrm{~mm}$. If the flow speed is(a) $1 \mathrm{~m} / \mathrm{s}$ (b) $4 \mathrm{~m} / \mathrm{s}$, compute the corresponding Froude
A partially open sluice gate in a 5 -m-wide rectangular channel carries water at $10 \mathrm{~m}^{3} / \mathrm{s}$. The upstream depth is $2.5 \mathrm{~m}$. Find the downstream depth and Froude
Find the critical depth for flow at $3 \mathrm{~m}^{3} / \mathrm{s}$ in a rectangular channel of width $2.5 \mathrm{~m}$.
Flow occurs in a rectangular channel of $6 \mathrm{~m}$ width and has a specific energy of $3 \mathrm{~m}$. Plot accurately the relation between depth and specific energy. Determine from the
What is the maximum flow rate that may occur in a rectangular channel $2.4 \mathrm{~m}$ wide for a specific energy of $1.5 \mathrm{~m}$ ?
A rectangular channel carries a discharge of $10 \mathrm{ft}^{3} / \mathrm{s}$ per foot of width. Determine the minimum specific energy possible for this flow. Compute the corresponding flow depth
Flow in the channel of Problem 11.15 has a specific energy of $4.5 \mathrm{ft}$. Compute the alternate depths for this specific energy.Data From Problem 11.15 11.15 A rectangular channel carries a
Consider the Venturi flume shown. The bed is horizontal, and flow may be considered frictionless. The upstream depth is $1 \mathrm{ft}$, and the downstream depth is $0.75 \mathrm{ft}$. The
Eleven cubic meters per second of water are diverted through ports in the bottom of the channel between sections (1) and (2). Neglecting head losses and assuming a horizontal channel, what depth of
A rectangular channel $10 \mathrm{ft}$ wide carries $100 \mathrm{cfs}$ on a horizontal bed at $1.0 \mathrm{ft}$ depth. A smooth bump across the channel rises $4 \mathrm{in}$. above the
At what depths can $800 \mathrm{cfs}$ flow in a trapezoidal channel of base width $12 \mathrm{ft}$ and side slopes 1 (vert.) on 3 (horiz.) if the specific energy is $7 \mathrm{ft}$ ?
At a section of a 10 -ft-wide rectangular channel, the depth is $0.3 \mathrm{ft}$ for a discharge of $20 \mathrm{ft}^{3} / \mathrm{s}$. A smooth bump $0.1 \mathrm{ft}$ high is placed on the
Water, at $3 \mathrm{ft} / \mathrm{s}$ and $2 \mathrm{ft}$ depth, approaches a smooth rise in a wide channel. Estimate the stream depth after the $0.5 \mathrm{ft}$ rise. V = 3 ft S y=2 ft
A horizontal rectangular channel $3 \mathrm{ft}$ wide contains a sluice gate. Upstream of the gate the depth is $6 \mathrm{ft}$ and the depth downstream is $0.9 \mathrm{ft}$. Estimate the
A hydraulic jump occurs in a rectangular channel $4.0 \mathrm{~m}$ wide. The water depth before the jump is $0.4 \mathrm{~m}$ and after the jump is $1.7 \mathrm{~m}$. Compute the flow rate in
A hydraulic jump occurs in a wide horizontal channel. The discharge is $2 \mathrm{~m}^{3} / \mathrm{s}$ per meter of width. The upstream depth is $500 \mathrm{~mm}$. Determine the depth of the
A hydraulic jump occurs in a rectangular channel. The flow rate is $200 \mathrm{ft}^{3} / \mathrm{s}$, and the depth before the jump is $1.2 \mathrm{ft}$. Determine the depth behind the jump and
The depths of water upstream and downstream from a hydraulic jump on the horizontal "apron" downstream from a spillway structure are observed to be approximately $3 \mathrm{ft}$ and \(8
Calculate $y_{2}, h$, and $y_{3}$ for this two-dimensional flow picture. State any assumptions clearly. Hydraulic jump $2 1.5 m 0.3 m P11.28
The hydraulic jump may be used as a crude flow meter. Suppose that in a horizontal rectangular channel $5 \mathrm{ft}$ wide the observed depths before and after a hydraulic jump are \(0.66
A hydraulic jump occurs on a horizontal apron downstream from a wide spillway at a location where depth is $0.9 \mathrm{~m}$ and speed is $25 \mathrm{~m} / \mathrm{s}$. Estimate the depth and
A hydraulic jump occurs in a rectangular channel. The flow rate is $50 \mathrm{~m}^{3} / \mathrm{s}$ and the depth before the jump is $2 \mathrm{~m}$. Determine the depth after the jump and the
A positive surge wave, or moving hydraulic jump, can be produced in the laboratory by suddenly opening a sluice gate. Consider a surge of depth $y_{2}$ advancing into a quiescent channel of depth
A 2-m-wide rectangular channel with a bed slope of 0.0005 has a depth of flow of $1.5 \mathrm{~m}$. Manning's roughness coefficient is 0.015 . Determine the steady uniform discharge in the channel.
Determine the uniform flow depth in a rectangular channel $2.5 \mathrm{~m}$ wide with a discharge of $3 \mathrm{~m}^{3} / \mathrm{s}$. The slope is 0.0004 and Manning's roughness factor is 0.015 .
Determine the uniform flow depth in a trapezoidal channel with a bottom width of $8 \mathrm{ft}$ and side slopes of 1 vertical to 2 horizontal. The discharge is \(100 \mathrm{ft}^{3} /
Water flows uniformly at a depth of $1.2 \mathrm{~m}$ in a rectangular canal $3 \mathrm{~m}$ wide laid on a slope of $1 \mathrm{~m}$ per $1000 \mathrm{~m}$. What is the mean shear stress on
This large uniform open channel flow is to be modeled without geometric distortion in the hydraulic laboratory at a scale of 1:9. What flow rate, bottom slope, and Manning $n$ will be required in
A rectangular flume built of timber is $3 \mathrm{ft}$ wide. The flume is to handle a flow of $90 \mathrm{ft}^{3} / \mathrm{s}$ at a normal depth of $6 \mathrm{ft}$. Determine the slope
A channel with square cross section is to carry $20 \mathrm{~m}^{3} / \mathrm{s}$ of water at normal depth on a slope of 0.003 . Compare the dimensions of the channel required for(a) concrete (b)
A triangular channel with side angles of $45^{\circ}$ is to carry $10 \mathrm{~m}^{3} / \mathrm{s}$ at a slope of 0.001 . The channel is concrete. Find the required dimensions.
A flume of timber has as its cross section an isosceles triangle (apex down) of $2.4 \mathrm{~m}$ base and $1.8 \mathrm{~m}$ altitude. At what depth will $5 \mathrm{~m}^{3} / \mathrm{s}$ flow
At what depth will $4.25 \mathrm{~m}^{3} / \mathrm{s}$ flow uniformly in a rectangular channel $3.6 \mathrm{~m}$ wide lined with rubble masonry and laid on a slope of $1: 4000$ ?
A semicircular trough of corrugated steel, with diameter $D=1 \mathrm{~m}$, carries water at depth $y=0.25 \mathrm{~m}$. The slope is 0.01 . Find the discharge.
A rectangular flume built of concrete with $1 \mathrm{ft}$ per $1000 \mathrm{ft}$ slope is $6 \mathrm{ft}$ wide. Water flows at a normal depth of $3 \mathrm{ft}$. The flume is fitted with a
Water flows in a trapezoidal channel at a flow rate of $10 \mathrm{~m}^{3} / \mathrm{s}$. The bottom width is $2.4 \mathrm{~m}$, the sides slope at $1: 1$, and the bed slope is 0.00193 . The
What slope is necessary to carry $11 \mathrm{~m}^{3} / \mathrm{s}$ uniformly at a depth of $1.5 \mathrm{~m}$ in a rectangular channel $3.6 \mathrm{~m}$ wide having $n=0.017$ ?
Find the normal depth for the channel of Problem 11.45 after a new plastic liner is installed.Data From Problem 11.45 11.45 Water flows in a trapezoidal channel at a flow rate of 10 m/s. The bottom
For a trapezoidal shaped channel with $n=0.014$ and slope $S_{b}=0.0002$ with a 20 -ft bottom width and side slopes of 1 vertical to 1.5 horizontal, determine the normal depth for a discharge of
Compute the critical depth for the channel in Problem 11.33.Data From Problem 11.33 11.33 A 2-m-wide rectangular channel with a bed slope of 0.0005 has a depth of flow of 1.5 m. Manning's roughness
A trapezoidal canal lined with brick has side slopes of $2: 1$ and bottom width of $10 \mathrm{ft}$. It carries $600 \mathrm{ft}^{3} / \mathrm{s}$ at critical speed. Determine the critical
An optimum rectangular storm sewer channel made of unfinished concrete is to be designed to carry a maximum flow rate of $100 \mathrm{ft}^{3} / \mathrm{s}$ at the critical flow rate (the rate at
For a sharp-crested suppressed weir of length $B=8.0 \mathrm{ft}$, $P=2.0 \mathrm{ft}$, and $H=1.0 \mathrm{ft}$, determine the discharge over the weir. Neglect the velocity of approach head.
A rectangular sharp-crested weir with end contractions is $1.5 \mathrm{~m}$ long. How high should the weir crest be placed in a channel to maintain an upstream depth of $2.5 \mathrm{~m}$ for
What is the depth of water behind a rectangular sharp-crested weir $1.5 \mathrm{~m}$ wide and $1.2 \mathrm{~m}$ high when a flow of $0.28 \mathrm{~m}^{3} / \mathrm{s}$ passes over it? What is
A broad-crested weir $0.9 \mathrm{~m}$ high has a flat crest and a coefficient of 1.6. If this weir is $6 \mathrm{~m}$ long and the head on it is $0.46 \mathrm{~m}$, what is the flow rate?
The head on $\mathrm{a} 90^{\circ} \mathrm{V}$-notch weir is $1.5 \mathrm{ft}$. Determine the discharge.
The geometry of a centrifugal water pump is $r_{1}=10 \mathrm{~cm}$, $r_{2}=20 \mathrm{~cm}, b_{1}=b_{2}=4 \mathrm{~cm}, \beta_{1}=30^{\circ}, \beta_{2}=15^{\circ}$, and it runs at speed \(1600
Find the resulting $\Pi$-groups when (a) $D, ho$, and $Q$ or (b) $H, ho$, and $Q$ are the repeating variables in the analysis of a turbomachine where the relevant variables are \(P, D, N,
Consider the centrifugal pump impeller dimensions given in Example 10.1. Estimate the ideal head rise and mechanical power input if the outlet blade angle is changed to \(60^{\circ}, 70^{\circ},
Dimensions of a centrifugal pump impeller areThe pump is driven at $575 \mathrm{rpm}$ and the fluid is water. Calculate the theoretical head and mechanical power if the flow rate is \(80,000
Dimensions of a centrifugal pump impeller areThe pump is driven at $1250 \mathrm{rpm}$ while pumping water. Calculate the theoretical head and mechanical power input if the flow rate is \(1500
The blade is one of a series. Calculate the force exerted by the jet on the blade system. 50 mm d water jet 45 m/s 30 m/s P10.6
This blade is one of a series. What force is required to move the series horizontally against the direction of the jet of water at a velocity of $15 \mathrm{~m} / \mathrm{s}$ ? What power is
A centrifugal water pump, with 15 -cm-diameter impeller and axial inlet flow, is driven at $1750 \mathrm{rpm}$. The impeller vanes are backward curved $\left(\beta_{2}=65^{\circ}\right)$ and have
Consider the centrifugal pump impeller dimensions given in Example 10.1. Construct the velocity diagram for shockless flow at the impeller inlet, if $b=$ constant. Calculate the effective flow
A centrifugal water pump designed to operate at $1300 \mathrm{rpm}$ has dimensionsDraw the inlet velocity diagram for a volume flow rate of $35 \mathrm{~L} / \mathrm{s}$. Determine the inlet
A series of blades, such as in Example 10.13, moving in the same direction as a water jet of $25 \mathrm{~mm}$ diameter and of velocity $46 \mathrm{~m} / \mathrm{s}$, deflects the jet
In passing through this blade system, the absolute jet velocity decreases from 41.5 to $22.5 \mathrm{~m} / \mathrm{s}$. If the flow rate is $57 \mathrm{~L} / \mathrm{s}$ of water, calculate the
A centrifugal pump runs at $1750 \mathrm{rpm}$ while pumping water at a rate of $50 \mathrm{~L} / \mathrm{s}$. The water enters axially, and leaves tangential to the impeller blades. The impeller
A centrifugal water pump designed to operate at $1200 \mathrm{rpm}$ has dimensionsDetermine the flow rate at which the entering velocity has no tangential component. Draw the outlet velocity
Kerosene is pumped by a centrifugal pump. When the flow rate is $350 \mathrm{gpm}$, the pump requires $18 \mathrm{hp}$ input and its efficiency is 82 percent. Calculate the pressure rise produced
In the water pump of Problem 10.8, the pump casing acts as a diffuser, which converts 60 percent of the absolute velocity head at the impeller outlet to static pressure rise. The head loss through
Use data from Appendix $C$ to choose points from the performance curves for a Peerless horizontal split case Type 16A18B pump at 705 and 880 nominal rpm. Obtain and plot curve-fits of total head
Data from tests of a water suction pump operated at $2000 \mathrm{rpm}$ with a 12 -in.-diameter impeller arePlot the performance curves for this pump; include a curve of efficiency versus volume
A centrifugal pump impeller having $r_{1}=50 \mathrm{~mm}$, $r_{2}=150 \mathrm{~mm}$, and width $b=3.75 \mathrm{~mm}$ is to pump $225 \mathrm{~L} / \mathrm{s}$ of water and supply \(12.2
A centrifugal pump impeller having dimensions and angles as shown rotates at $500 \mathrm{rpm}$. Assuming a radial direction of velocity at the blade entrance, calculate the flow rate, the pressure
An axial-flow fan operates in sea-level air at $1350 \mathrm{rpm}$ and has a blade tip diameter of $3 \mathrm{ft}$ and a root diameter of $2.5 \mathrm{ft}$. The inlet angles are
Data measured during tests of a centrifugal pump driven at $3000 \mathrm{rpm}$ areThe flow rate is $65 \mathrm{gpm}$ and the torque applied to the pump shaft is \(4.75 \mathrm{lbf} \cdot
A small centrifugal pump, when tested at $N=2875 \mathrm{rpm}$ with water, delivered $Q=0.016 \mathrm{~m}^{3} / \mathrm{s}$ and $H=40 \mathrm{~m}$ at its best efficiency point $(\eta=0.70)$.
If the impeller of Problem 10.20 rotates between horizontal planes of infinite extent and the flow rate is $25 \mathrm{~L} / \mathrm{s}$, what rise of pressure may be expected between one point
At the outlet of a pump impeller of diameter $0.6 \mathrm{~m}$ and width $150 \mathrm{~mm}$, the absolute velocity is observed to be $30 \mathrm{~m} / \mathrm{s}$ at an angle of $60^{\circ}$
Typical performance curves for a centrifugal pump, tested with three different impeller diameters in a single casing, are shown. Specify the flow rate and head produced by the pump at its best
A pump with $D=500 \mathrm{~mm}$ delivers $Q=0.725 \mathrm{~m}^{3} / \mathrm{s}$ of water at $H=10 \mathrm{~m}$ at its best efficiency point. If the specific speed of the pump is 1.74 , and the
At its best efficiency point $(\eta=0.87)$, a mixed-flow pump, with $D=16$ in., delivers $Q=2500 \mathrm{cfm}$ of water at $H=140 \mathrm{ft}$ when operating at $N=1350 \mathrm{rpm}$.
Using the performance curves in Appendix C, select the smallest diameter Peerless 8AE20G pump operating at $1770 \mathrm{rpm}$ that will deliver a flow of at least $2000 \mathrm{gpm}$ for the
A pump (Peerless 8AE20G, Appendix C) operates at 1775 rpm and has the 20 -in. inch impeller. It supplies the pipe-line below while operating at maximum efficiency. Find the pipeline loss coefficient
A pumping system must be specified for a lift station at a wastewater treatment facility. The average flow rate is 110 million liters per day and the required lift is $10 \mathrm{~m}$. Non-clogging
A centrifugal water pump operates at $1750 \mathrm{rpm}$; the impeller has backward-curved vanes with $\beta_{2}=60^{\circ}$ and $b_{2}=1.25 \mathrm{~cm}$. At a flow rate of \(0.025
A set of eight $30-\mathrm{kW}$ motor-pump units is used to deliver water through an elevation of $30 \mathrm{~m}$. The efficiency of the pumps is specified to be 65 percent. Estimate the
A blower has a rotor with 12-in. outside diameter and 10-in. inside diameter with 1.5 -in high rotor blades. The flow rate through the blower is $500 \mathrm{ft}^{3} / \mathrm{min}$ at a rotor
A centrifugal water pump has an impeller with an outer diameter of $14 \mathrm{in}$. and a blade height of $1 \mathrm{in}$. It rotates at 1200 $\mathrm{rpm}$. The flow enters parallel to the
Appendix C contains area bound curves for pump model selection and performance curves for individual pump models. Use these data to verify the similarity rules for a Peerless Type 4AE12 pump, with
Consider the Peerless Type 16A18B horizontal split case centrifugal pump (Appendix C). Use these performance data to verify the similarity rules for(a) impeller diameter change (b) operating speeds
Use data from Appendix $C$ to verify the similarity rules for the effect of changing the impeller diameter of a Peerless Type 4AE12 pump operated at 1750 and 3550 nominal rpm.Data From Appendix C
A centrifugal water pump has an impeller with backwardcurved vanes and an inner diameter of $0.1 \mathrm{~m}$, an outer diameter of $0.25 \mathrm{~m}$, and a blade height of $4 \mathrm{~cm}$.
Catalog data for a centrifugal water pump at design conditions are $Q=250 \mathrm{gpm}$ and $\Delta p=18.6 \mathrm{psi}$ at $1750 \mathrm{rpm}$. A laboratory flume requires $200 \mathrm{gpm}$
$ \mathrm{~A} 1 / 3$ scale model of a centrifugal water pump running at $N_{m}=5100 \mathrm{rpm}$ produces a flow rate of $Q_{m}=1 \mathrm{~m}^{3} / \mathrm{s}$ with a head of \(H_{m}=5.4
Sometimes the variation of water viscosity with temperature can be used to achieve dynamic similarity. A model pump delivers $0.10 \mathrm{~m}^{3} / \mathrm{s}$ of water at \(15^{\circ}
A large deep fryer at a snack-food plant contains hot oil that is circulated through a heat exchanger by pumps. Solid particles and water droplets coming from the food product are observed in the
Data from tests of a pump, with a 12.3-in.-diameter impeller operated at $1450 \mathrm{rpm}$ areDevelop and plot a curve-fit equation for NPSHR versus volume flow rate in the form NPSHR \(=a+b
A four-stage boiler feed pump has suction and discharge lines of $10 \mathrm{~cm}$ and $7.5 \mathrm{~cm}$ inside diameter. At $3500 \mathrm{rpm}$, the pump is rated at \(0.025 \mathrm{~m}^{3} /
A centrifugal pump operating at $N=2265 \mathrm{rpm}$ lifts water between two reservoirs connected by $300 \mathrm{ft}$ of 6 -in.-diameter and $100 \mathrm{ft}$ of 3-in.-diameter cast-iron pipe
A centrifugal pump is installed in a piping system with $L=300 \mathrm{~m}$ of $D=40 \mathrm{~cm}$ cast-iron pipe. The downstream reservoir surface is $15 \mathrm{~m}$ lower than the upstream
Part of the water supply for the South Rim of Grand Canyon National Park is taken from the Colorado River [54]. A flow rate of $600 \mathrm{gpm}$ taken from the river at elevation \(3734
A pump transfers water from one reservoir to another through two cast-iron pipes in series. The first is $3000 \mathrm{ft}$ of 9-in.-diameter pipe and the second is $1000 \mathrm{ft}$ of
Performance data for a pump areEstimate the delivery when the pump is used to move water between two open reservoirs through $1200 \mathrm{ft}$ of 12-in.-diameter commercial steel pipe containing
Consider the pump and piping system of Problem 10.50. Determine the volume flow rate and gate valve loss coefficient for the case of two identical pumps installed in parallel.Data From Problem 10.50
Consider the pump and piping system of Problem 10.51. Estimate the percentage reductions in volume flow rate that occur after(a) 20 years (b) 40 years of use, if the pump characteristics remain
Consider the flow system shown in Problem 8.94. Assume the minimum NPSHR at the pump inlet is $15 \mathrm{ft}$ of water. Select a pump appropriate for this application. Use the data for increase in

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