Consider the gate shown in Fig. P2.79. The gate is masslessand has a width b

Obtain a photograph/image of a situation in which the hydrostatic force on a plane surface is important. Print this photo and write a brief paragraph that describes the situation involved

The basic elements of a hydraulic press are shown in Fig. P2.68. The plunger has an area of 1 in.2 , and a force, F1, can be applied to the plunger through a lever mechanism having a mechanical advantage of 8 to 1. If the large piston has an area of 150 in.2 , what load, F2, can be raised by a force of 30 lb applied to the lever? Neglect the hydrostatic pressure variation.

The hydraulic cylinder shown in Fig. P2.69, with a 4-in.- diameter piston, is advertised as being capable of providing a force of F = 20 tons. If the piston has a design pressure (the maximum pressure at which the cylinder should safely operate) of 2500 lbin2 , gage, can the cylinder safely provide the advertised force?

A Bourdon gage (see Fig. 2.13 and Video V2.4) 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 weight, , placed on one side with the gage on the other side. The weight acting on the liquid through a 0.4-in.-diameter opening creates a pressure that is transmitted to the gage. This arrangement, with a series of weights, can be used to determine what a change in the dial movement, , in Fig. P2.70b, corresponds to in terms of a change in pressure. For a particular gage, some data are given below. Based on a plot of these data, determine the relationship between and the pressure, p, where p is measured in psi. (lb) 0 1.04 2.00 3.23 4.05 5.24 6.31 (deg.) 0 20 40 60 80 100 120

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 lb of force. Explain how a 20-lb force can be converted into hundreds or thousands of pounds of force, and why this does not violate our general perception that you cant get something for nothing (a somewhat loose paraphrase of the first law of thermodynamics). Hint: Consider the work done by each force.

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 1 2-in. plywood weighs approximately 36 lb. If the machines end effector has a diameter of 5 in., determine the suction pressure required to lift the sheet, expressed in inches of H2O suction.

A piston having a cross-sectional area of 0.07 m2 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. For h1 = 60 mm and h = 100 mm, what is the value of the applied force, P, acting on the piston? The weight of the piston is negligible.

A 6-in.-diameter piston is located within a cylinder that is connected to a 1 2-in.-diameter inclined-tube manometer as shown in Fig. P2.74. The fluid in the cylinder and the manometer is oil (specific weight = 59 lbft3 ). When a weight, , is placed on the top of the cylinder, the fluid level in the manometer tube rises from point (1) to (2). How heavy is the weight? Assume that the change in position of the piston is negligible.

The container shown in Fig. P2.75 has square cross sections. Find the vertical force on the horizontal surface, ABCD.

Find the weight needed to hold the wall shown in Fig. P2.76 upright. The wall is 10 m wide.

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.

An automobile has just dropped into a river. The car door is approximately a rectangle, measures 36 in. wide and 40 in. high, and hinges on a vertical side. The water level inside the car is up to the midheight of the door, and the air inside the car is at atmospheric pressure. Calculate the force required to open the door if the force is applied 24 in. from the hinge line. See Fig. P2.78. (The driver did not have the presence of mind to open the window to escape.)

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 the hinge, and the hydrostatic pressure on the horizontal side (or bottom) creates a clockwise moment about the hinge. Show that the net clockwise moment is u = wghb( 2 2 h2 6 ).

Will the gate in Problem 44 ever open?

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.

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, p1, within the container that will open the hatch. Neglect the weight of the hatch and friction in the hinge.

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 the forms is 85 lb, and the specific weight of the concrete is 150 lb/ft3

A long, vertical wall separates seawater from fresh water. If the seawater stands at a depth of 7 m, what depth of freshwater is required to give a zero resultant force on the wall? When the resultant force is zero, will the moment due to the fluid forces be zero? Explain.

Forms used to make a concrete basement wall are shown in Fig. P2.85. Each 4-ft-long form is held together by four tiestwo at the top and two at the bottom as indicated. Determine the tension in the upper and lower ties. Assume concrete acts as a fluid with a weight of 150 lb /ft3 .

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 sections (A, B, and C) of the wooden forms (neglect any restraining force of the two ends of the forms).

A homogeneous, 4-ft-wide, 8-ft-long rectangular gate weighing 800 lb is held in place by a horizontal flexible cable as shown in Fig. P2.87. Water acts against the gate, which is hinged at point A. Friction in the hinge is negligible. Determine the tension in the cable.

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 gate, determine the magnitude of the fluid force on the rectangular portion of the gate above the shaft and the magnitude of the fluid force on the semicircular portion of the gate below the shaft. (b) For this same fluid depth determine the moment of the force acting on the semicircular portion of the gate with respect to an axis that coincides with the shaft.

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 AA and is held shut against the water pressure by a latch at B. Show that the force on the latch is independent of the supply pressure, p, and the height of the tank, h.

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 this pressure difference can be if it is not too difficult for an average person to open the door.

Find the center of pressure of an elliptical area of minor axis 2a and major axis 2b where axis 2a is vertical and axis 2b is horizontal. The center of the ellipse is a vertical distance h below the surface of the water (h > a). The fluid density is constant. Will the center of pressure of the ellipse change if the fluid is replaced by another constant-density fluid? Will the center of pressure of the ellipse change if the vertical axis is tilted back an angle from the vertical about its horizontal axis? Explain.

The dam shown in Fig. P2.92 is 200 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 force.

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.

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 tailwater inclined wall of the dam. Note that the slope given is the ratio of the run to the rise. Consider a unit length of the dam (b = 1 ft).

The Keswick dam in Problem 2.94 is made of concrete and has a specific weight of 150 lb/ft3 . The hydrostatic forces and the weight of the dam produce a total vertical force of the dam on the foundation. Find the magnitude and location of this total vertical force. Consider a unit length of the dam (b = 1 ft).

The Keswick dam in Problem 2.94 is made of concrete and has a specific weight of 150 lb/ft3 . The coefficient of friction between the base of the dam and the foundation is 0.65. Is the dam likely to slide downstream? Consider a unit length of the dam (b = 1 ft).

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 dam and on the tailwater wall of the dam. Note that the slope given is the ratio of the run to the rise. Consider a unit length of the dam (b = 1 ft).

The Altus dam in Problem 2.97 is made of concrete with a density of 150 lbm/ft3 . The coefficient of friction between the base of the dam and the foundation is 0.65. Is the dam likely to slide downstream? Consider a unit length of the dam (b = 1 ft).

Find the magnitude and location of the net horizontal force on the gate shown in Fig. P2.99. The gate width is 5.0 m.

Find the magnitude and location of the net vertical force on the gate in Problem 2.99.

Find the total vertical force on the cylinder shown in Fig. P2.101.

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 and held closed by a horizontal force, FH, located at the center of the gate. The maximum value for FH is 3500 kN. (a) Determine the maximum water depth, h, above the center of the gate that can exist without the gate opening. (b) Is the answer the same if the gate is hinged at the top? Explain your answer.

A gate having the cross section shown in Fig. P2.103 is 4 ft wide and is hinged at C. The gate weighs 18,000 lb, and its mass center is 1.67 ft to the right of the plane BC. Determine the vertical reaction at A on the gate when the water level is 3 ft above the base. All contact surfaces are smooth.

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 lb counterweight, . Determine the water depth, h.

A 200-lb homogeneous gate 10 ft wide and 5 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 moved to the right, the water level remains at the top of the gate. The line of action of the force that the brace exerts on the gate is along the brace. (a) Plot the magnitude of the force exerted on the gate by the brace as a function of the angle of the gate, , for 0 90. (b) Repeat the calculations for the case in which the weight of the gate is negligible. Comment on the result as 0.

An open tank has a vertical partition and on one side contains gasoline with a density = 700 kg/m3 at a depth of 4 m, as shown in Fig. P2.106. A rectangular gate that is 4 m high and 2 m wide and hinged at one end is located in the partition. Water is slowly added to the empty side of the tank. At what depth, h, will the gate start to open?

A horizontal 2-m-diameter conduit is half filled with a liquid (SG = 1.6) and is capped at both ends with plane vertical surfaces. The air pressure in the conduit above the liquid surface is 200 kPa. Determine the resultant force of the fluid acting on one of the end caps, and locate this force relative to the bottom of the conduit.

A 4-ft by 3-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 from the frictionless hinge is just sufficient to keep the gate closed when the water depth is 2 ft, that is, when the water fills the semicircular lower portion of the tank. If the water were deeper, the gate would open. Determine the 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 drain pipe that contains air at atmospheric pressure. Determine the minimum water depth, h, at which the gate will pivot to allow water to flow into the pipe.

The closed vessel of Fig. P2.110 contains water with an air pressure of 10 psi at the water surface. One side of the vessel contains a spout that is closed by a 6-in.-diameter circular gate that is hinged along one side as illustrated. The horizontal axis of the hinge is located 10 ft below the water surface. Determine the minimum torque that must be applied at the hinge to hold the gate shut. Neglect the weight of the gate and friction at the hinge.

(See The Wide World of Fluids article titled The Three Gorges Dam, Section 2.8.) (a) Determine the horizontal hydrostatic force on the 2309-m-long Three Gorges Dam when the average depth of the water against it is 175 m. (b) If all of the 6.4 billion people on Earth were to push horizontally against the Three Gorges Dam, could they generate enough force to hold it in place? Support your answer with appropriate calculations.