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engineering
engineering fluid mechanics

Questions and Answers of Engineering Fluid Mechanics

A Bourdon gage (see Fig. 2.13) is often used to measure pressure. One way to calibrate this type of gage is to use the arrangement shown in Fig. P2.70a. The container is filled with a liquid and a
A bottle jack allows an average person to lift one corner of a 4000-lb automobile completely off the ground by exerting less than \(20 \mathrm{lb}\) of force. Explain how a 20-lb force can be
Suction is often used in manufacturing processes to lift objects to be moved to a new location. A 4 -ft by 8 -ft sheet of \(\frac{1}{2}\)-in. plywood weighs approximately \(36 \mathrm{lb}\). If the
A piston having a cross-sectional area of \(0.07 \mathrm{~m}^{2}\) is located in a cylinder containing water as shown in Fig. P2.73. An open U-tube manometer is connected to the cylinder as shown.
A 6-in.-diameter piston is located within a cylinder that is connected to a \(\frac{1}{2}\)-in.-diameter inclined-tube manometer as shown in Fig. P2.74. The fluid in the cylinder and the manometer is
The container shown in Fig. P2.75 has square cross sections. Find the vertical force on the horizontal surface, \(A B C D\).Figure P2.75 2- B C A D E Water 23 HIN F IN
Find the weight \(\mathscr{W}\) needed to hold the wall shown in Fig. P2.76 upright. The wall is \(10 \mathrm{~m}\) wide.Figure P2.76 Water W 3 m Wall 4 m Pinned
Determine the magnitude and direction of the force that must be applied to the bottom of the gate shown in Fig. P2.77 to keep the gate closed.Figure P2.77 2.1 m Water Hinge 2-m-wide gate 0.8 m
An automobile has just dropped into a river. The car door is approximately a rectangle, measures \(36 \mathrm{in}\). wide and \(40 \mathrm{in}\). high, and hinges on a vertical side. The water level
Consider the gate shown in Fig. P2.79. The gate is massless and has a width \(b\) (perpendicular to the paper). The hyprostatic pressure on the vertical side creates a counterclockwise moment about
Will the gate in Problem 44 ever open?Problem 44A flowrate measuring device is installed in a horizontal pipe through which water is flowing. A U-tube manometer is connected to the pipe through
A tank contains 6 in. of oil \((S=0.82)\) above 6 in. of water \((S=1.00)\). Find the force on the bottom of the tank. See Fig. P2.81.Figure P2. 81 |-A=1 ft Oil (S=0.82) Water (S= 1.0)
A structure is attached to the ocean floor as shown in Fig. P2.82. A 2-m-diameter hatch is located in an inclined wall and hinged on one edge. Determine the minimum air pressure, \(p_{1}\), within
Concrete is poured into the forms as shown in Fig. P2.83 to produce a set of steps. Determine the weight of the sandbag needed to keep the bottomless forms from lifting off the ground. The weight of
A long, vertical wall separates seawater from fresh water. If the seawater stands at a depth of \(7 \mathrm{~m}\), what depth of freshwater is required to give a zero resultant force on the wall?
Forms used to make a concrete basement wall are shown in Fig. P2.85. Each 4-ft-long form is held together by four ties-two at the top and two at the bottom as indicated. Determine the tension in the
While building a high, tapered concrete wall, builders used the wooden forms shown in Fig. P2.86. If concrete has a specific gravity of about 2.5, find the total force on each of the three side
A homogeneous, 4-ft-wide, 8-ft-long rectangular gate weighing \(800 \mathrm{lb}\) is held in place by a horizontal flexible cable as shown in Fig. P2.87. Water acts against the gate, which is hinged
A gate having the shape shown in Fig. P2.88 is located in the vertical side of an open tank containing water. The gate is mounted on a horizontal shaft.(a) When the water level is at the top of the
A pump supplies water under pressure to a large tank as shown in Fig. P2.89. The circular-plate valve fitted in the short discharge pipe on the tank pivots about its diameter \(A-A\) and is held shut
Sometimes it is difficult to open an exterior door of a building because the air distribution system maintains a pressure difference between the inside and outside of the building. Estimate how big
Find the center of pressure of an elliptical area of minor axis \(2 a\) and major axis \(2 b\) where axis \(2 a\) is vertical and axis \(2 b\) is horizontal. The center of the ellipse is a vertical
The dam shown in Fig. P2.92 is \(200 \mathrm{ft}\) long and is made of concrete with a specific gravity of 2.2. Find the magnitude and \(y\) coordinate of the line of action of the net horizontal
Repeat Problem 2.92 but find the magnitude and \(x\) coordinate of the line of action of the vertical force on the dam resulting from the water.Problem 2.92The dam shown in Fig. P2.92 is \(200
Figure P2.94 is a representation of the Keswick gravity dam in California. Find the magnitudes and locations of the hydrostatic forces acting on the headwater vertical wall of the dam and on the
The Keswick dam in Problem 2.94 is made of concrete and has a specific weight of \(150 \mathrm{lb} / \mathrm{ft}^{3}\). The hydrostatic forces and the weight of the dam produce a total vertical
The Keswick dam in Problem 2.94 is made of concrete and has a specific weight of \(150 \mathrm{lb} / \mathrm{ft}^{3}\). The coefficient of friction \(\mu\) between the base of the dam and the
Figure P2.97 is a representation of the Altus gravity dam in Oklahoma. Find the magnitudes and locations of the horizontal and vertical hydrostatic force components acting on the headwater wall of
The Altus dam in Problem 2.97 is made of concrete with a density of \(150 \mathrm{lbm} / \mathrm{ft}^{3}\). The coefficient of friction \(\mu\) between the base of the dam and the foundation is 0.65.
Find the magnitude and location of the net horizontal force on the gate shown in Fig. P2.99. The gate width is \(5.0 \mathrm{~m}\).Figure P2.99 4.0 m Water 11.0m A 45 B-2.0 m- 2.0 m Water 3.0 m
Find the magnitude and location of the net vertical force on the gate in Problem 2.99.Problem 2.99.Find the magnitude and location of the net horizontal force on the gate shown in Fig. P2.99. The
Find the total vertical force on the cylinder shown in Fig. P2.101.Figure P2. 101 Patm |D=6cm- 18 cm 3 cm 5 cm d= 3 cm Water
A 3-m-wide, 8-m-high rectangular gate is located at the end of a rectangular passage that is connected to a large open tank filled with water as shown in Fig. P2.102. The gate is hinged at its bottom
A gate having the cross section shown in Fig. P2.103 is \(4 \mathrm{ft}\) wide and is hinged at \(C\). The gate weighs \(18,000 \mathrm{lb}\), and its mass center is \(1.67 \mathrm{ft}\) to the right
The massless, 4-ft-wide gate shown in Fig. P2.104 pivots about the frictionless hinge O. It is held in place by the \(2000 \mathrm{lb}\) counterweight, \(\mathscr{W}\). Determine the water depth,
A 200-lb homogeneous gate \(10 \mathrm{ft}\) wide and \(5 \mathrm{ft}\) long is hinged at point \(A\) and held in place by a 12 -ft-long brace as shown in Fig. P2.105. As the bottom of the brace is
An open tank has a vertical partition and on one side contains gasoline with a density \(ho=700 \mathrm{~kg} / \mathrm{m}^{3}\) at a depth of \(4 \mathrm{~m}\), as shown in Fig. P2.106. A rectangular
A horizontal 2-m-diameter conduit is half filled with a liquid \((S G=1.6)\) and is capped at both ends with plane vertical surfaces. The air pressure in the conduit above the liquid surface is \(200
A 4 - \(\mathrm{ft}\) by 3 - \(\mathrm{ft}\) massless rectangular gate is used to close the end of the water tank shown in Fig. P2.108. A 200-lb weight attached to the arm of the gate at a distance
A thin 4-ft-wide, right-angle gate with negligible mass is free to pivot about a frictionless hinge at point \(O\), as shown in Fig. P2.109. The horizontal portion of the gate covers a 1 -ft-diameter
The closed vessel of Fig. P2.110 contains water with an air pressure of \(10 \mathrm{psi}\) at the water surface. One side of the vessel contains a spout that is closed by a 6 -in.-diameter circular
The Wide World of Fluids article titled "The Three Gorges Dam,".(a) Determine the horizontal hydrostatic force on the 2309-m-long Three Gorges Dam when the average depth of the water against it is
Obtain a photograph/image of a situation in which the hydrostatic force on a curved surface is important. Print this photo and write a brief paragraph that describes the situation involved.
A 2-ft-diameter hemispherical plexiglass "bubble" is to be used as a special window on the side of an above-ground swimming pool. The window is to be bolted onto the vertical wall of the pool and
Consider the curved surface shown in Fig. P2.114 (a) and (b). The two curved surfaces are identical. How are the vertical forces on the two surfaces alike? How are they different?Figure P2. 114 (9) 3
Figure P2.115 shows a cross section of a submerged tunnel used by automobiles to travel under a river. Find the magnitude and location of the resultant hydrostatic force on the circular roof of the
The container shown in Fig. P2.116 has circular cross sections. Find the vertical force on the inclined surface. Also find the net vertical force on the bottom, \(E F\). Is the vertical force equal
The 18-ft-long lightweight gate of Fig. P2.117 is a quarter circle and is hinged at \(H\). Determine the horizontal force, \(P\), required to hold the gate in place. Neglect friction at the hinge and
The air pressure in the top of the 2-liter pop bottle shown in Video V2.6 and Fig. P2.118 is 40 psi, and the pop depth is \(10 \mathrm{in}\). The bottom of the bottle has an irregular shape with a
In drilling for oil in the Gulf of Mexico, some divers have to work at a depth of \(1300 \mathrm{ft}\).(a) Assume that seawater has a constant density of \(64 \mathrm{lb} / \mathrm{ft}^{3}\) and
Hoover Dam (see Video 2.5) is the highest arch-gravity type of dam in the United States. A cross section of the dam is shown in Fig. P2.120(a). The walls of the canyon in which the dam is located are
A plug in the bottom of a pressurized tank is conical in shape, as shown in Fig. P2.121. The air pressure is \(40 \mathrm{kPa}\), and the liquid in the tank has a specific weight of \(27 \mathrm{kN}
The homogeneous gate shown in Fig. P2.122 consists of one quarter of a circular cylinder and is used to maintain a water depth of \(4 \mathrm{~m}\). That is, when the water depth exceeds \(4
The concrete (specific weight \(=150 \mathrm{lb} / \mathrm{ft}^{3}\) ) seawall of Fig. P2.123 has a curved surface and restrains seawater at a depth of 24 ft. The trace of the surface is a parabola
A step-in viewing window having the shape of a half-cylinder is built into the side of a large aquarium. See Fig. P2.124. Find the magnitude, direction, and location of the net horizontal forces on
Find the magnitude, direction, and location of the net vertical force acting on the viewing window in Problem 2.124.Problem 2.124A step-in viewing window having the shape of a half-cylinder is built
A 10-m-long log is stuck against a dam, as shown in Fig. P2.126. Find the magnitudes and locations of both the horizontal force and the vertical force of the water on the log in terms of the diameter
Find the net horizontal force on the 4.0-m-long log shown in Fig. P2.127.Figure P2.127 1.0 m D= 1.0 m 0.5 m
An open tank containing water has a bulge in its vertical side that is semicircular in shape as shown in Fig. P2.128. Determine the horizontal and vertical components of the force that the water
A closed tank is filled with water and has a 4 -ft-diameter hemispherical dome as shown in Fig. 2.129. A U-tube manometer is connected to the tank. Determine the vertical force of the water on the
A 3-m-diameter open cylindrical tank contains water and has a hemispherical bottom as shown in Fig. P2.130. Determine the magnitude, line of action, and direction of the force of the water on the
Three gates of negligible weight are used to hold back water in a channel of width \(b\) as shown in Fig. P2.131. The force of the gate against the block for gate \((b)\) is \(R\). Determine (in
Obtain a photograph/image of a situation in which Archimedes's principle is important. Print this photo and write a brief paragraph that describes the situation involved.
An iceberg (specific gravity 0.917) floats in the ocean (specific gravity 1.025). What percent of the volume of the iceberg is under water?
A floating 40-in.-thick piece of ice sinks 1 in. with a \(500-\mathrm{lb}\) polar bear in the center of the ice. What is the area of the ice in the plane of the water level? For seawater, \(S=1.03\).
A spherical balloon filled with helium at \(40^{\circ} \mathrm{F}\) and \(20 \mathrm{psia}\) has a 25 - \(\mathrm{ft}\) diameter. What load can it support in atmospheric air at \(40^{\circ}
A river barge, whose cross section is approximately rectangular, carries a load of grain. The barge is \(28 \mathrm{ft}\) wide and \(90 \mathrm{ft}\) long. When unloaded, its draft (depth of
A barge is \(40 \mathrm{ft}\) wide by \(120 \mathrm{ft}\) long. The weight of the barge and its cargo is denoted by \(W\). When in salt-free riverwater, it floats \(0.25 \mathrm{ft}\) deeper than
When the Tucurui Dam was constructed in northern Brazil, the lake that was created covered a large forest of valuable hardwood trees. It was found that even after 15 years underwater the trees were
Estimate the minimum water depth needed to float a canoe carrying two people and their camping gear. List all assumptions and show all calculations.
An inverted test tube partially filled with air floats in a plastic water-filled soft drink bottle as shown in Fig. P2.140. The amount of air in the tube has been adjusted so that it just floats. The
A child's balloon is a sphere \(1 \mathrm{ft}\). in diameter. The balloon is filled with helium \(\left(ho=0.014 \mathrm{lbm} / \mathrm{ft}^{3}\right)\). The balloon material weighs \(0.008
A 1-ft-diameter, 2-ft-long cylinder floats in an open tank containing a liquid having a specific weight \(\gamma\). A U-tube manometer is connected to the tank as shown in Fig. P2.142. When the
A not-too-honest citizen is thinking of making bogus gold bars by first making a hollow iridium ( \(S=22.5)\) ingot and plating it with a thin layer of gold \((S=19.3)\) of negligible weight and
A solid cylindrical pine \((S=0.50)\) spar buoy has a cylindrical lead \((S=11.3)\) weight attached, as shown in Fig. P2.144. Determine the equilibrium position of the spar buoy in seawater (i.e.,
When a hydrometer (see Fig. P2.145) having a stem diameter of \(0.30 \mathrm{in}\). is placed in water, the stem protrudes \(3.15 \mathrm{in}\). above the water surface. If the water is replaced with
A 2-ft-thick block constructed of wood \((S G=0.6)\) is submerged in oil \((S G=0.8)\) and has a 2-ft-thick aluminum (specific weight \(=168 \mathrm{lb} / \mathrm{ft}^{3}\) ) plate attached to the
A submarine is modeled as a cylinder with a length of \(300 \mathrm{ft}\), a diameter of \(50 \mathrm{ft}\), and a conning tower as shown in Fig. P2.148. The submarine can dive a distance of \(50
The Wide World of Fluids article titled "Concrete canoes,". How much extra water does a 147-1b concrete canoe displace compared to an ultralightweight 38-1b Kevlar canoe of the same size carrying the
Obtain a photograph/image of a situation in which the pressure variation in a fluid with rigid-body motion is involved. Print this photo and write a brief paragraph that describes the situation
When an automobile brakes, the fuel gage indicates a fuller tank than when the automobile is traveling at a constant speed on a level road. Is the sensor for the fuel gage located near the front or
An open container of oil rests on the flatbed of a truck that is traveling along a horizontal road at \(55 \mathrm{mi} / \mathrm{hr}\). As the truck slows uniformly to a complete stop in \(5
A 5-gal, cylindrical open container with a bottom area of 120 in. \(^{2}\) is filled with glycerin and rests on the floor of an elevator.(a) Determine the fluid pressure at the bottom of the
A plastic glass has a square cross section measuring \(2 \frac{1}{2}\) in. on a side and is filled to within \(1 / 2\) in. of the top with water. The glass is placed in a level spot in a car with two
The cylinder in Fig. P2.154 accelerates to the left at the rate of \(9.80 \mathrm{~m} / \mathrm{s}^{2}\). Find the tension in the string connecting at rod of circular cross section to the cylinder.
A closed cylindrical tank that is \(8 \mathrm{ft}\) in diameter and \(24 \mathrm{ft}\) long is completely filled with gasoline. The tank, with its long axis horizontal, is pulled by a truck along a
The cart shown in Fig. P2.156 measures \(10.0 \mathrm{~cm}\) long and \(6.0 \mathrm{~cm}\) high and has rectangular cross sections. It is half-filled with water and accelerates down a \(20^{\circ}\)
The U-tube manometer in Fig. P2.157 is used to measure the acceleration of the cart on which it sits. Develop an expression for the acceleration of the cart in terms of the liquid height \(h\), the
A tank has a height of \(5.0 \mathrm{~cm}\) and a square cross section measuring \(5.0 \mathrm{~cm}\) on a side. The tank is one third full of water and is rotated in a horizontal plane with the
An open 1-m-diameter tank contains water at a depth of \(0.7 \mathrm{~m}\) when at rest. As the tank is rotated about its vertical axis the center of the fluid surface is depressed. At what angular
A child riding in a car holds a string attached to a floating, helium-filled balloon. As the car decelerates to a stop, the balloon tilts backwards. As the car makes a right-hand turn, the balloon
A closed, 0.4-m-diameter cylindrical tank is completely filled with oil \((S G=0.9)\) and rotates about its vertical longitudinal axis with an angular velocity of \(40 \mathrm{rad} / \mathrm{s}\).
The Wide World of Fluids article titled "Rotating mercury mirror telescope,". The largest liquid mirror telescope uses a 6-ft-diameter tank of mercury rotating at \(7 \mathrm{rpm}\) to produce its
Obtain a photograph/image of a situation that can be analyzed by use of the Bernoulli equation. Print this photo and write a brief paragraph that describes the situation involved. Bernoulli equation
Water flows steadily through the variable area horizontal pipe shown in Fig. P3.3. The centerline velocity is given by \(\mathbf{V}=\) \(10(1+x) \hat{\mathbf{i}} \mathrm{ft} / \mathrm{s}\), where
Air flows steadily along a streamline from point (1) to point (2) with negligible viscous effects. The following conditions are measured: At point (1) \(z_{1}=2 \mathrm{~m}\) and \(p_{1}=0
What pressure gradient along the streamline, \(d p / d s\), is required to accelerate water in a horizontal pipe at a rate of \(30 \mathrm{~m} / \mathrm{s}^{2}\) ?
At a given location the airspeed is \(20 \mathrm{~m} / \mathrm{s}\) and the pressure gradient along the streamline is \(100 \mathrm{~N} / \mathrm{m}^{3}\). Estimate the airspeed at a point \(0.5
An incompressible fluid flows steadily past a circular cylinder as shown in Fig. P3.8. The fluid velocity along the dividing streamline \((-\infty \leq x \leq-a)\) is found to be
Consider a compressible liquid that has a constant bulk modulus. Integrate "F = ma" along a streamline to obtain the equivalent of the Bernoulli equation for this flow. Assume steady, inviscid flow.

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