Questions and Answers of Introduction To Fluid Mechanics

A horizontal nozzle having a cylindrical tip of \(75 \mathrm{~mm}\) diameter attached to a \(150-\mathrm{mm}\)-diameter water pipe discharges \(0.05 \mathrm{~m}^{3} / \mathrm{s}\). In the pipe just
When \(0.3 \mathrm{~m}^{3} / \mathrm{s}\) of water flows through a \(150-\mathrm{mm}\)-diameter constriction in a \(300-\mathrm{mm}\)-diameter horizontal pipeline, the pressure at a point in the pipe
The Colebrook equation (Eq. 8.37) for computing the turbulent friction factor is implicit in \(f\). An explicit expression [31] that gives reasonable accuracy is\[f_{0}=0.25\left[\log \left(\frac{e /
We saw in Section 8.7 that instead of the implicit Colebrook equation (Eq. 8.37) for computing the turbulent friction factor \(f\), an explicit expression that gives reasonable accuracy is
Water flows through a 2-in.-diameter tube that suddenly contracts to \(1 \mathrm{in}\). diameter. The pressure drop across the contraction is 0.5 psi. Determine the volume flow rate.
A 50-mm-diameter nozzle terminates a vertical \(150-\mathrm{mm}-\) diameter pipeline in which water flows downward. At a point on the pipeline a pressure gage reads \(276 \mathrm{kPa}\). If this
A 12-in.-diameter pipe leaves a reservoir of surface elevation 300 at elevation 250 and drops to elevation 150, where it terminates in a 3-in.-diameter nozzle. If the head lost through line and
A water pipe gradually changes from 6 -in.-diameter to 8 -in.diameter accompanied by an increase of elevation of \(10 \mathrm{ft}\). If the pressures at the 6 in. and 8 in. sections are 9 psi and 6
Air at standard conditions flows through a sudden expansion in a circular duct. The upstream and downstream duct diameters are \(75 \mathrm{~mm}\) and \(225 \mathrm{~mm}\), respectively. The pressure
Water flows from a larger pipe, diameter \(D_{1}=100 \mathrm{~mm}\), into a smaller one, diameter \(D_{2}=50 \mathrm{~mm}\), by way of a reentrant device. Find the head loss between points (1) and
Flow through a sudden contraction is shown. The minimum flow area at the vena contracta is given in terms of the area ratio by the contraction coefficient
A flow rate of \(1.01 / \mathrm{min}\) of oil of specific gravity 0.92 exists in this pipeline. Is this flow laminar? What is the viscosity of the oil? For the same flow in the opposite direction,
Water flows in a smooth pipeline at a Reynolds number of \(10^{6}\). After many years of use, it is observed that half the original flow rate produces the same head loss as for the original flow.
Air flows out of a clean room test chamber through a \(150-\mathrm{mm}-\) diameter duct of length \(L\). The original duct had a square-edged entrance, but this has been replaced with a well-rounded
A conical diffuser is used to expand a pipe flow from a diameter of \(100 \mathrm{~mm}\) to a diameter of \(150 \mathrm{~mm}\). Find the minimum length of the diffuser if we want a loss coefficient
By applying the basic equations to a control volume starting at the expansion and ending downstream, analyze flow through a sudden expansion assuming that the inlet pressure \(p_{1}\) acts on the
Water at \(45^{\circ} \mathrm{C}\) enters a shower head through a circular tube with \(15.8 \mathrm{~mm}\) inside diameter. The water leaves in 24 streams, each of \(1.05 \mathrm{~mm}\) diameter. The
Water discharges to atmosphere from a large reservoir through a moderately rounded horizontal nozzle of \(35-\mathrm{mm}\)-diameter. The free surface is \(2.5 \mathrm{~m}\) above the nozzle exit
You are asked to compare the behavior of fully developed laminar flow and fully developed turbulent flow in a horizontal pipe under different conditions. For the same flow rate, which will have the
A laboratory experiment is set up to measure pressure drop for flow of water through a smooth tube. The tube diameter is \(15.9 \mathrm{~mm}\), and its length is \(3.56 \mathrm{~m}\). Flow enters the
The applied pressure difference, \(\Delta p\), and corresponding volume flow rate, \(Q\), for laminar flow in a tube can be compared to the applied DC voltage \(V\) across, and current \(I\) through,
Plot the required reservoir depth of water to create flow in a smooth tube of diameter \(10 \mathrm{~mm}\) and length \(100 \mathrm{~m}\), for a flow rate range of \(1 \mathrm{~L} / \mathrm{min}\)
Oil with kinematic viscosity \(u=7.5 \times 10^{-4} \mathrm{ft}^{2} / \mathrm{s}\) flows at \(45 \mathrm{gpm}\) in a 100-ft-long horizontal drawn-tubing pipe of \(1 \mathrm{in}\). diameter. By what
Water from a pump flows through a 9-in.-diameter commercial steel pipe for a distance of 4 miles from the pump discharge to a reservoir open to the atmosphere. The level of the water in the reservoir
A 5 -cm-diameter potable water line is to be run through a maintenance room in a commercial building. Three possible layouts for the water line are proposed, as shown. Which is the best option, based
A system for testing variable-output pumps consists of the pump, four standard elbows, and an open gate valve forming a closed circuit as shown. The circuit is to absorb the energy added by the pump.
Two reservoirs are connected by three clean cast-iron pipes in series, \(L_{1}=600 \mathrm{~m}, D_{1}=0.3 \mathrm{~m}, L_{2}=900 \mathrm{~m}, D_{2}=0.4 \mathrm{~m}\), \(L_{3}=1500 \mathrm{~m}\), and
Water, at volume flow rate \(Q=0.75 \mathrm{ft}^{3} / \mathrm{s}\), is delivered by a fire hose and nozzle assembly. The hose of \(L=250 \mathrm{ft}, D=3\) in., and \(e / D=0.004\) is made up of four
Flow in a tube may alternate between laminar and turbulent \(\square\) states for Reynolds numbers in the transition zone. Design a bench-top experiment consisting of a constant-head cylindrical
When you drink a beverage with a straw, you need to overcome both gravity and friction in the straw. Estimate the fraction of the total effort you put into quenching your thirst of each factor,
What flow rate (gpm) will be produced in a 75 -mm-diameter water pipe for which there is a pressure drop of \(425 \mathrm{kPa}\) over a \(200-\mathrm{m}\) length? The pipe roughness is \(2.5
You recently bought a house and want to improve the flow rate of water on your top floor. The low flow rate is due to three reasons: The city water pressure at the water meter is low ( \(p=200
Gasoline flows in a long, underground pipeline at a constant temperature of \(15^{\circ} \mathrm{C}\). Two pumping stations at the same elevation are located \(13 \mathrm{~km}\) apart. The pressure
An 18-in.-diameter new riveted steel pipeline \(1000 \mathrm{ft}\) long runs from an elevation of \(150 \mathrm{ft}\) to an elevation of \(200 \mathrm{ft}\). If the pressure at \(150 \mathrm{ft}\) is
What diameter of smooth masonry pipe is needed to carry \(50 \mathrm{cfs}\) between two reservoirs of surface elevations 250 and 100 if the pipeline is to be 2 miles long?
Laboratory tests on cylindrical pipe yield the empirical forrnula \(h_{L}=0.002583 \mathrm{lV}^{2.14} d^{-0.86}\) with head loss, length, and diameter in \(\mathrm{m}\), and velocity in \(\mathrm{m}
Water flows steadily in a 125 -mm-diameter cast-iron pipe \(150 \mathrm{~m}\) long. The pressure drop between sections (1) and (2) is \(150 \mathrm{kPa}\), and section (2) is located \(15
Two galvanized iron pipes of diameter \(D\) are connected to a large water reservoir, as shown. Pipe \(A\) has length \(L\) and pipe \(B\) has length \(2 L\). Both pipes discharge to atmosphere.
A mining engineer plans to do hydraulic mining with a highspeed jet of water. A lake is located \(H=300 \mathrm{~m}\) above the mine site. Water will be delivered through \(L=900 \mathrm{~m}\) of
The flow of water through a 150-mm-diameter horizontal pipe that enlarges abruptly to \(300 \mathrm{~mm}\) diameter, is \(0.14 \mathrm{~m}^{3} / \mathrm{s}\). The pressure in the smaller pipe is
The fluid flowing has specific gravity \(0.90 ; V_{75}=6 \mathrm{~m} / \mathrm{s}\); \(\mathbf{R}=10^{5}\). Calculate the gage reading. 45 m. El. 27 m 2.4 m 140 kpa 75 mm d--150 mm d- Smooth P8.111
Water is flowing. Calculate the direction and magnitude of the manometer reading. 3 in. 6 in. d 60 in. 12 in. d V = 10 ft/s Mercury- P8.112
Investigate the effect of tube roughness on flow rate by computing the flow generated by a pressure difference \(\Delta p=100 \mathrm{kPa}\) applied to a length \(L=100 \mathrm{~m}\) of tubing, with
Investigate the effect of tube length on water flow rate by computing the flow generated by a pressure difference \(\Delta p=100 \mathrm{kPa}\) applied to a length \(L\) of smooth tubing, of diameter
For the pipe flow into a reservoir of Example 8.5 consider the effect of pipe roughness on flow rate, assuming the pressure of the pump is maintained at \(153 \mathrm{kPa}\). Plot the flow rate
Calculate the magnitude and direction of the manometer reading. Water is flowing. V -3 m 2.4 m 75 mm dy = 4.5 m/s f = 0.020 -Mercury P8.116 444 0.9 m
Experimental determination of local losses and loss coefficients are made from measurements of the hydraulic grade lines in zones of established flow. Calculate the head loss and loss coeffecients
Water is flowing. Calculate the gage reading when the velocity in the 12 -in.-diameter pipe is \(8 \mathrm{ft} / \mathrm{s}\). Elevation 170 ft Elevation=200 ft 8 ft, 6-in.-diameter, 150 ft,
The siphon shown is fabricated from 50-mm-ID drawn aluminum tubing. The liquid is water at \(15^{\circ} \mathrm{C}\). Compute the volume flow rate through the siphon. Estimate the minimum pressure
A large open water tank has a horizontal cast iron drainpipe of diameter \(D=1 \mathrm{in}\). and length \(L=2 \mathrm{ft}\) attached at its base. If the depth of water is \(h=3 \mathrm{ft}\), find
A tank containing \(30 \mathrm{~m}^{3}\) of kerosene is to be emptied by a gravity feed using a drain hose of diameter \(15 \mathrm{~mm}\), roughness \(0.2 \mathrm{~mm}\), and length \(1
A \(90^{\circ}\) screwed elbow is installed in a 2-in.-diameter pipeline having a friction factor of 0.03 . The head lost at the elbow is equivalent to that lost in how many feet of the pipe? What
Calculate the total tension in the bolts. Neglect entrance loss. The pipe is \(30 \mathrm{~m}\) long, the diameter is \(150 \mathrm{~mm}\), and \(f=0.020\). 6 m Bolts Water P8.123
A horizontal 50-mm-diameter PVC pipeline leaves (squareedged entrance) a water tank \(3 \mathrm{~m}\) below its free surface. At \(15 \mathrm{~m}\) from the tank, it enlarges abruptly to a 100
You are watering your lawn with an old hose. Because lime deposits have built up over the years, the 0.75 -in.-ID. hose now has an average roughness height of \(0.022 \mathrm{in}\). One
Your boss claims that for pipe flow the flow rate, \(Q \propto \sqrt{\Delta p}\), where \(\Delta p\) is the pressure difference driving the flow. You dispute this, so perform some calculations. You
A hydraulic press is powered by a remote high-pressure pump. The gage pressure at the pump outlet is \(3000 \mathrm{psi}\), whereas the pressure required for the press is 2750 psi gage, at a flow
One-quarter of a cubic meter per second of liquid at \(20^{\circ} \mathrm{C}\) is to be carried between two tanks having a difference of surface elevation of \(9 \mathrm{~m}\). If the pipeline is
Calculate the flow rate from this water tank if the 6 in. pipeline has a friction factor of 0.020 and is \(50 \mathrm{ft}\) long. Is cavitation to be expected in the pipe entrance? The water in the
A 6-ft-diameter pipeline 4 miles long between two reservoirs of surface elevations 500 and \(300 \mathrm{ft}\) carries a flow rate of \(250 \mathrm{cfs}\) of water \(\left(68^{\circ}
Determine the minimum size smooth rectangular duct with an aspect ratio of 3 that will pass \(1 \mathrm{~m}^{3} / \mathrm{s}\) of \(10^{\circ} \mathrm{C}\) air with a head loss of \(25 \mathrm{~mm}\)
A new industrial plant requires a water flow rate of \(5.7 \mathrm{~m}^{3} / \mathrm{min}\). The gage pressure in the water main, located in the street \(50 \mathrm{~m}\) from the plant, is \(800
What diameter water pipe is required to handle \(0.075 \mathrm{~m}^{3} / \mathrm{s}\) and a \(500 \mathrm{kPa}\) pressure drop? The pipe length is \(175 \mathrm{~m}\), and roughness is \(2.5
A pipe friction experiment for air consists of a smooth brass tube with \(63.5 \mathrm{~mm}\) inside diameter; the distance between pressure taps is \(1.52 \mathrm{~m}\). The pressure drop is
Oil has been flowing from a large tank on a hill to a tanker at the wharf. The compartment in the tanker is nearly full and an operator is in the process of stopping the flow. A valve on the wharf is
The pressure rise across a water pump is \(35 \mathrm{psi}\) when the volume flow rate is \(500 \mathrm{gpm}\). If the pump efficiency is 80 percent, determine the power input to the pump.
Cooling water is pumped from a reservoir to rock drills on a construction job using the pipe system shown. The flow rate must be \(600 \mathrm{gpm}\) and water must leave the spray nozzle at \(120
You are asked to size a pump for installation in the water supply system of the Willis Tower (formerly the Sears Tower) in Chicago. The system requires \(100 \mathrm{gpm}\) of water pumped to a
Heavy crude oil ( \(\mathrm{SG}=0.925\) and \(u=1.0 \times 10^{-4} \mathrm{~m}^{2} / \mathrm{s}\) ) is pumped through a pipeline laid on flat ground. The line is made from steel pipe with \(600
Petroleum products are transported over long distances by pipelines such as the Alaskan pipeline (see Example 8.6). Estimate the energy needed to pump a typical petroleum product, expressed as a
A water pump can generate a pressure difference \(\Delta p\) (psi) given by \(\Delta p=145-0.1 Q^{2}\), where the flow rate is \(Q \mathrm{ft}^{3} / \mathrm{s}\). It supplies a pipe of diameter \(20
The head versus capacity curve for a certain fan may be approximated by the equation \(H=30-10^{-7} Q^{2}\), where \(H\) is the output static head in inches of water and \(Q\) is the air flow rate in
A swimming pool has a partial-flow filtration system. Water at \(75^{\circ} \mathrm{F}\) is pumped from the pool through the system shown. The pump delivers \(30 \mathrm{gpm}\). The pipe is nominal
Water at \(65^{\circ} \mathrm{C}\) flows through a 75 -mm-diameter orifice installed in a \(150-\mathrm{mm}-\mathrm{ID}\) pipe. The flow rate is \(20 \mathrm{~L} / \mathrm{s}\). Determine the
A smooth \(200-\mathrm{m}\) pipe, \(100 \mathrm{~mm}\) diameter connects two reservoirs. The entrance and exit of the pipe are sharp-edged. At the midpoint of the pipe is an orifice plate with
A 12 in. \(\times 6\) in. Venturi meter is installed in a horizontal waterline. The pressure gages read 30 and 20 psi. Calculate the flow rate for a water temperature of \(68^{\circ} \mathrm{F}\) and
A 1-in.-diameter nozzle is attached to a 3-in.-diameter hose. What flow rate of water will occur through the nozzle when the pressure in the hose is \(60 \mathrm{psi}\) ? Assume that the Reynolds
A sharp-edged orifice with conventional pressure connections and an orifice coefficient of \(K=0.6\) is to be installed in a \(300-\mathrm{mm}\)-diameter waterline. For a flow rate of \(0.28
A venturi meter with a 3-in.-diameter throat is placed in a 6 -in.-diameter line carrying water at \(75^{\circ} \mathrm{F}\). The pressure drop between the upstream tap and the venturi throat is \(12
Air flows through a venturi meter with a 3-in.-diameter throat placed in a 6-in.-diameter line. Assume that the upstream pressure is \(60 \mathrm{psi}\) and the temperature is \(68^{\circ}
Water at \(10^{\circ} \mathrm{C}\) flows steadily through a venturi. The pressure upstream from the throat is \(200 \mathrm{kPa}\) gage. The throat diameter is \(50 \mathrm{~mm}\); and the upstream
Drinking straws are to be used to improve the air flow in a pipe-flow experiment. Packing a section of the air pipe with drinking straws to form a "laminar flow element" might allow the air flow rate
In some western states, water for mining and irrigation was sold by the "miner's inch," the rate at which water flows through an opening in a vertical plank of \(1 \mathrm{in.}^{2}\) area, up to \(4
A rice farmer needs to fill a \(150 \mathrm{~m} \times 400 \mathrm{~m}\) field with water to a depth of \(7.5 \mathrm{~cm}\) in \(1 \mathrm{hr}\). How many 37.5-cm-diameter supply pipes are needed if
Water flows steadily past a porous flat plate. Constant suction is applied along the porous section. The velocity profile at section \(c d\) is
A tank of fixed volume contains brine with initial density, \(ho_{i}\), greater than water. Pure water enters the tank steadily and mixes thoroughly with the brine in the tank. The liquid level in
A conical funnel of half-angle \(\theta=30^{\circ}\) drains through a small hole of diameter \(d=6.25 \mathrm{~mm}\). at the vertex. The speed of the liquid leaving the funnel is \(V=\sqrt{2 g y}\),
Evaluate the net rate of flux of momentum out through the control surface of Problem 4.22.Data From Problem 4.22 4.22 Fluid with 1040 kg/m density is flowing steadily through the rectangular box
Water flows steadily through a pipe of length \(L\) and radius \(R=75 \mathrm{~mm}\). The velocity distribution across the outlet is given by\[u=u_{\max }\left[1-\frac{r^{2}}{R^{2}}\right]\]and
Evaluate the net momentum flux through the bend of Problem 4.34, if the depth normal to the diagram is \(w=1 \mathrm{~m}\).Data From Problem 4.34 4.34 A two-dimensional reducing bend has a linear
Evaluate the net momentum flux through the channel of Problem 4.35. Would you expect the outlet pressure to be higher, lower, or the same as the inlet pressure? Why?Data From Problem 4.35 4.35 Water
A conical enlargement in a vertical pipeline is \(5 \mathrm{ft}\) long and enlarges the pipe diameter from 12 in. to 24 in. Calculate the magnitude and direction of the vertical force on this
A 100-mm nozzle is bolted (with 6 bolts) to the flange of a \(300-\mathrm{mm}\)-diameter horizontal pipeline and discharges water into the atmosphere. Calculate the tension load on each bolt when the
The projectile partially fills the end of the \(0.3 \mathrm{~m}\) pipe. Calculate the force required to hold the projectile in position when the mean velocity in the pipe is \(6 \mathrm{~m} /
Considering that in the fully developed region of a pipe, the integral of the axial momentum is the same at all cross sections, explain the reason for the pressure drop along the pipe.
A jet of water issuing from a stationary nozzle at \(10 \mathrm{~m} / \mathrm{s}\left(A_{j}=0.1 \mathrm{~m}^{2}\right)\) strikes a turning vane mounted on a cart as shown. The vane turns the jet
A circular cylinder inserted across a stream of flowing water deflects the stream through angle \(\theta\), as shown. (This is termed the "Coanda effect.") For \(a=12.5 \mathrm{~mm}, b=2.5
A 6-in.-diameter horizontal pipeline bends through \(90^{\circ}\) and while bending changes its diameter to 3 in. The pressure in the 6-in. pipe is 30 psi. Calculate the magnitude and direction of
The axes of the pipes are in a vertical plane. The flow rate is \(2.83 \mathrm{~m}^{3} / \mathrm{s}\) of water. Calculate the magnitude, direction, and location of the resultant force of the water on
Water flows through a tee in a horizontal pipe system. The velocity in the stem of the tee is \(15 \mathrm{ft} / \mathrm{s}\), and the diameter is \(12 \mathrm{in}\). Each branch is of 6 in.

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