The variation of pressure with density in a thick gas

Problem 142P The density of a floating body can be determined bytying weights to the body until both the body and the weights are completely submerged, and then weighing them separately in air. Consider a wood log that weighs 1540 N in air. If it takes 34 kg of lead (? = 11,300 kg/m3) to completed sink the log and the lead in water, determine the average density of the log.

Problem 156P The average density of icebergs is about 917 kg/m3. (a) Determine the percentage of the total volume of an iceberg submerged in seawater of density 1042 kg/m3. (b) Although icebergs are mostly submerged, they are observed to turn over. Explain how this can happen. (Hint: Consider the temperatures of icebergs and seawater.)

Problem 141P An oil pipeline and a 1.3–m3 rigid air tank are connected to each other by a manometer, as shown in Fig. P3–149. If the tank contains 15 kg of air at 80°C. determine (a) the absolute pressure in the pipeline and (b) the change in ?h when the temperature in the tank drops to 20°C. Assume the pressure in the oil pipeline to remain constant, and the air volume in the manometer to be negligible relative to the volume of the tank.

Problem 152P A 5–m–long, 4–m–high tank contains 2.5–m–deep water when not in motion and is open to the atmosphere through a vent in the middle. The tank is now accelerated to the right on a level surface at 2 m/s2. Determine the maximum pressure in the tank relative to the atmospheric pressure.

Problem 146P Repeat Prob. 10-41 for a total water height of 2 m. PROBLEM: A 3-m-high, 6-m-wide rectangular gate is hinged at the top edge at A and is restrained by a fixed ridge at B determine the hydrostatic force exerted on the gate by the 5-m-high water and the location of the pressure center.

Problem 18P The barometer of a mountain hiker reads 930 mbars at the beginning of a hiking trip and 820 mbars at the end. Neglecting the effect of altitude on local gravitational acceleration, determine the vertical distance climbed. Assume an average air density of 1.20 kg/m3.

Problem 154P An elastic air balloon having a diameter of 30 cm is attached to the base of a container partially filled with water at +4°C, as shown in Fig. P10-46. If the pressure of air above water is gradually increased from 100 kPa to 1.6 MPa, will the force on the cable change? If so, what is the percent change in the force? Assume the pressure on the free surface and the diameter of the balloon are related by P = CDn, where C is a constant and n = ?2. The weight of the balloon and the air in it is negligible.

The basic barometer can be used to measure the height of a building. If the barometric readings at the top and at the bottom of a building are 730 and 755 mmHg, respectively, determine the height of the building. Assume an average air density of 1.18 \(\mathrm{kg} / \mathrm{m}^{3}\).

Problem 20P Solve Prob. 3–22 using EES (or other) software. Print out the entire solution, including the numerical results with proper units, and take the density of mercury to be 13,600 kg/m3.

Problem 21P Determine the pressure exerted on a diver at 20 m below the free surface of the sea. Assume a barometric pressure of 101 kPa and a specific gravity of 1.03 for seawater.

Problem 24P Reconsider Prob. 3–26. Using EES (or other) eH! software, investigate the effect of the spring force in the range of 0 to 500 N on the pressure inside the cylinder. Plot the pressure against the spring force, and discuss the results.

Problem 26P Reconsider Prob. 3–28. Using EES (or other) MM software, investigate the effect of the manometer fluid density in the range of 800. to 13,000 kg/m3 on the differential fluid height of the manometer. Plot the differential fluid height against the density, and discuss the results.

Problem 58P A submerged horizontal flat plate is suspended in water by a string attached at the centroid of its upper surface. Now the plate is rotated 45° about an axis that passes through its centroid. Discuss the change on the hydrostatic force acting on the. top surface of this plate as a result of this rotation. Assume the plate remains submerged at all times.

Problem 25P Both a gage and a manometer are attached to a gas tank to measure its pressure. If the reading on the pressure gage is 65 kPa, determine the distance between the two fluid levels of the manometer if the fluid is(a) mercury (? = 13,600 kg/m3) or (b) water (? = 1000 kg/m3).

A gas is contained in a vertical, frictionless piston–cylinder device. The piston has a mass of 4 kg and a cross– sectional area of 35 \(\mathrm{Cm}^{2}\). A compressed spring above the piston exerts a force of 60 N on the piston. If the atmospheric pressure is 95 kPa, determine the pressure inside the cylinder.

Problem 57P Someone claims that she can determine the magnitude of the hydrostatic force acting on a plane surface submerged in water regardless of its shape and orientation if she knew the vertical distance of the centroid of the surface from the free surface and the area of the surface. Is this a valid claim? Explain.

Problem 59P You may have noticed that dams are much thicker at the bottom. Explain why dams are built that way.

Problem 60P Consider a submerged curved surface. Explain how you would determine the horizontal component of the hydrostatic force acting on this surface.

Problem 61P Consider a submerged curved surface. Explain how you would determine the vertical component of the hydrostatic force acting on this surface.

Problem 63P Consider a heavy car submerged in water in a lake with a flat bottom. The driver’s side door of the car is 1.1 m high and 0.9 m wide, and the top edge of the door is 10 m below the water surface. Determine the net force acting on the door (normal to its surface) and the location of the pressure center if (a) the car is well–sealed and it contains air at atmospheric pressure and (b) the car is filled with water.

Problem 62P Consider a circular surface subjected to hydrostatic forces by a constant density liquid. If the magnitudes of the horizontal and vertical components of the resultant hydrostatic force are determined, explain how you would find the line of action of this force.

Problem 64P Consider a 4-m-long, 4-m-wide, and 1.5-m-high aboveground swimming pool that is fdled with water to the rim. (a) Determine the hydrostatic force on each wall and the distance of the line of action of this force from the ground. (b) If the height of the walls of the pool is doubled and the pool is filled, will the hydrostatic force on each wall double or quadruple? Why?

Problem 66P A room in the lower level of a cruise ship has a 30–cm–diameter circular window. If the midpoint of the window is 4 m below the water surface, determine the hydrostatic force acting on the window, and the pressure center. Take the specific gravity of seawater to be 1.025.

A 4-m-long quarter-circular gate of radius 3 m and of negligible weight is hinged about its upper edge A, as shown in Fig. P10-23. The gate controls the flow of water over the ledge at B, where the gate is pressed by a spring. Determine the minimum spring force required to keep the gate closed when the water level rises to A at the upper edge of the gate.

Problem 96P One of the common procedures in fitness programs is to determine the fat-to-muscle ratio of the body. This is based on the principle that the muscle tissue is denser than the fat tissue, and, thus, the higher the average density of the body, the higher is the fraction of muscle tissue. The average density of the body can be determined by weighing the person in air and also while submerged in water in a tank. Treating all tissues and bones (other than fat) as muscle with an equivalent density of ?muscle, obtain a relation for the volume fraction of body fat xfat.

Problem 95P It is said that Archimedes discovered his principle during a bath while thinking about how he could determine if King Hiero’s crown was actually made of pure gold. While in the bathtub, he conceived the idea that he could determine the average density of an irregularly shaped object by weighing it in air and also in water. If the crown weighed 3.20 kgf (= 31.4 N) in air and 2.95 kgf (= 28.9 N) in water, determine if the crown is made of pure gold. The density of gold is 19,300 kg/m3. Discuss how you can solve this problem without weighing the crown in water but by using an ordinary bucket with no calibration for volume. You may weigh anything in air.

Problem 99P Consider a glass of water. Compare the water pressures at the bottom surface for the following cases: the glass is (a) stationary, (b) moving up at constant velocity, (c) moving down at constant velocity, and (d) moving horizontally at constant velocity.

Problem 97P The hull of a boat has a volume of 150 m3, and the total mass of the boat when empty is 8560 kg. Determine how much load this boat can carry without sinking (a) in a lake and (b) in seawater with a specific gravity of 1.03.

Problem 98P Under what conditions can a moving body of fluid be treated as a rigid body?

Problem 100P Consider two identical glasses of water, one stationary and the other moving on a horizontal plane with constant acceleration. Assuming no splashing or spilling occurs, which glass will have a higher pressure at the (a) front, (b) midpoint, and (c) back of the bottom surface?

Problem 101P Consider a vertical cylindrical container partially filled with water. Now the cylinder is rotated about its axis at a specified angular velocity, and rigid–body motion is established. Discuss how the pressure will be affected at the midpoint and at the edges of the bottom surface due to rotation.

Problem 103P Consider two water tanks filled with water. The first tank is 8 m high and is stationary, while the second tank is 2 m high and is moving upward with an acceleration of 5 m/s2. Which tank will have a higher pressure at the bottom?

Problem 102P A water tank is being towed by a truck on a level road, and the angle the free surface makes with the horizontal is measured to be 12°. Determine the acceleration of the truck.

Problem 104P A water tank is being towed on an uphill road that makes 20° with the horizontal with a constant acceleration of 5 m/s2 in the direction of motion. Determine the angle the free surface of water makes with the horizontal. What would your answer be if the direction of motion were downward on the same road with the same acceleration?

Problem 112P The distance between the centers of the two arms of a U–tube open to the atmosphere is 30 cm, and the U–tube contains 20–cm–high alcohol in both arms. Now the U–tube is rotated about the left arm at 4.2 rad/s. Determine the elevation difference between the fluid surfaces in the two arms.

Problem 106P A 60-cm-high, 40-cm-diameter cylindrical water tank is being transported on a level road. The highest acceleration anticipated is 4 m/s2. Determine the allowable initial water height in the tank if no water is to spill out during acceleration.

A gasoline line is connected to a pressure gage through a double-U manometer, as shown in Fig. P3–138. If the reading of the pressure gage is 370 kPa. determine the gage pressure of the gasoline line.

Problem 133P The pressure of water flowing through a pipe is measured by the arrangement shown in Fig. P3–141. For the values given, calculate the pressure in the pipe.

Problem 111P Repeat Prob. 3–116 for a deceleration of 2.5 m/s2. PROBLEM: Milk with a density of 1020 kg/m3 is transported on a level road in a 7–m–long, 3–m–diameter cylindrical tanker. The tanker is completely filled with milk (no air space), and it accelerates at 2.5 m/s2. If the minimum pressure in the tanker is 100 kPa, determine the maximum pressure difference and the location of the maximum pressure.

Problem 132P Repeat Prob. 3–138 for a pressure gage reading of 280 kPa.

Problem 134P Consider a U–tube filled with mercury as shown in Fig. P3–142. The diameter of the right arm of the U–tube is D = 2 cm. and the diameter of the left arm is twice that. Oil with a specific gravity of 2.72 is poured into the left arm, forcing some mercury from the left arm into the right one. Determine the maximum amount of oil that can be added into the left arm.

Problem 135P A teapot with a brewer at the top is used to brew tea, as shown in Fig. P3–143. The brewer may partially block the vapor from escaping, causing the pressure in the teapot to rise and an overflow from the service tube to occur. Disregarding thermal expansion and the variation in the amount of water in the service tube to be negligible relative to the amount of water in the teapot, determine the maximum coldwater height that would not cause an overflow at gage pressures of up to 0.32 kPa for the vapor.

Problem 136P Repeat Prob. 3–129 by taking the thermal expansion of water into consideration as it is heated from 20°C to the boiling temperature of 100°C.

Problem 137P It is well known that the temperature of the atmosphere varies with altitude. In the troposphere, which extends to an altitude of 11 km, for example, the variation of temperature can be approximated by where T0 is the temperature at sea level, which can be taken to be 288.15 K, and ? = 0.0065 K/m. The gravitational acceleration also changes with altitude as where g0 = 9.807 m/s2 and z is the elevation from sea level in m. Obtain a relation for the variation of pressure in the troposphere (a) by ignoring and (b) by considering the variation of g with altitude.

Problem 140P A system is equipped with two pressure gages and a manometer, as shown in Fig. P3–148. For ?h = 12 cm, determine the pressure difference

Problem 139P Pressure transducers are commonly used to measure pressure by generating analog signals usually in the range of 4 mA to 20 mA or 0 V-DC to 10 V-DC in response to applied pressure. The system whose schematic is shown in Fig. P3-147 can be used to calibrate pressure transducers. A rigid container is filled with pressurized air, and pressure is measured by the manometer attached. A valve is used to regulate the pressure in the container. Both the pressure and the electric signal are measured simultaneously for various settings, and the results are tabulated. For the given set of measurements, obtain the calibration curve in the form of P = al + b, where a and >> b are constants, and calculate the pressure that corresponds to a signal of 10 mA. ?h, mm 28.0 181.5 297.8 413.1 765.9 I, mA 4.21 5.78 6.97 8.15 11.76 ?h, mm 1027 1149 1362 1458 1536 I, mA 14.43 15.68 17.86 18.84 19.64

Problem 138P The variation of pressure with density in a thick gas layer is given by where C and n are constants. Noting that the pressure change across a differential fluid layer of thickness dz in the vertical z–direction is given as dP= ??g dz, obtain a relation for pressure as a function of elevation z. Take the pressure and density at z = 0 to be P0 and ?0, respectively.

Problem 27P A manometer containing oil (? = 850 kg/m3) is attached to a tank filled with air. If the oil–level difference between the two columns is 45 cm and the atmospheric pressure is 98 kPa, determine the absolute pressure of the air in the tank.

A mercury manometer \(\left(\rho=13,600\mathrm{\ kg}/\mathrm{m}^3\right)\) is connected to an air duct to measure the pressure inside. The difference in the manometer levels is 10 mm, and the atmospheric pressure is 100 kPa. (a) Judging from Fig. P3–31, determine if the pressure in the duct is above or below the atmospheric pressure, (b) Determine the absolute pressure in the duct.

Problem 29P Repeat Prob. 3–31 for a differential mercury height of 30 mm.

Problem 67P The water side of the wall of a 100-m-long dam is a quarter circle with a radius of 10 m. Determine the hydrostatic force on the dam and its line of action when the dam is filled to the rim.

Problem 68P A 6-m-high, 5-m-wide rectangular plate blocks the end of a 5-m-deep freshwater channel, as shown in Fig. P3–73. The plate is hinged about a horizontal axis along its upper edge through a point A and is restrained from opening by a fixed ridge at point B. Determine the force exerted on the plate by the ridge.

Problem 69P Reconsider Prob. 3–73. Using EES (or other) software, investigate the effect of water c.epth on the force exerted on the plate by the ridge. Let the water depth vary from 0 to 5 m in increments of 0.5 m. Tabulate and plot your results.

Problem 107P A 40-cm-diameter, 90-cm-high vertical cylindrical container is partially filled with 60-cm-high water. Now the cylinder is rotated at a constant angular speed of 120 rpm. Determine how much the liquid level at the center of the cylinder will drop as a result of this rotational motion.

Problem 108P A fish tank that contains 60–cm–high water is moved in the cabin of an elevator. Determine the pressure at the bottom of the tank when the elevator is (a) stationary, (b) moving up with an upward acceleration of 3 m/s2, and (c) moving down with a downward acceleration of 3 m/s2.

Problem 109P A 3–m–diameter vertical cylindrical milk tank rotates at a constant rate of 12 rpm. If the pressure at the center of the bottom surface is 130 kPa, determine the pressure at the edge of the bottom surface of the tank. Take the density of the milk to be 1030 kg/m3.

Problem 143P The 280–kg, 6–m–wide rectangular gate shown in Fig. P3–151 is hinged at B and leans against the floor at A making an angle of 45° with the horizontal. The gate is to be opened from its lower edge by applying a normal force at its center. Determine the minimum force F required to open the water gate.

Problem 144P Repeat Prob. 3–151 for a water height of 1.2 m above the hinge at B.

Problem 145P A 3-m-high, 6-m-wide rectangular gate is hinged at the top edge at A and is restrained by a fixed ridge at B determine the hydrostatic force exerted on the gate by the 5-m-high water and the location of the pressure center.

Problem 30P Blood pressure is usually measured by wrapping a closed air–filled jacket equipped with a pressure gage around the upper arm of a person at the level of the heart. Using a mercury manometer and a stethoscope, the systolic pressure (the maximum pressure when the heart is pumping) and the diastolic pressure (the minimum pressure when the heart is resting) are measured in mmHg. The systolic and diastolic pressures of a healthy person are about 120 mmHg and 80 mmHg, respectively, and are indicated as 120/80. Express both of these gage pressures in kPa, psi, and meter water column.

Problem 31P The maximum blood pressure in the upper arm of a healthy person is about 120 mmHg. If a vertical tube open to the atmosphere is connected to the vein in the arm of the person. determine how high the blood will rise in the tube. Take the density of the blood to be 1040 kg/m3.

Problem 32P Consider a 1.8–m–tall man standing vertically in water and completely submerged in a pool. Determine the difference between the pressures acting at the head and at the toes of this man. in kPa.

Problem 70P

Problem 71P

Problem 72P A water trough of semicircular cross section of radius 0.7 m consists of two symmetric parts hinged to each other at the bottom, as shown in Fig. P3–77. The two parts are held together by a cable and turnbuckle placed every 3 m along the length of the trough. Calculate the tension in each cable when the trough is filled to the rim.

Problem 110P Milk with a density of 1020 kg/m3 is transported on a level road in a 7–m–long, 3–m–diameter cylindrical tanker. The tanker is completely filled with milk (no air space), and it accelerates at 2.5 m/s2. If the minimum pressure in the tanker is 100 kPa, determine the maximum pressure difference and the location of the maximum pressure.

Problem 147P

Problem 33P Consider a U–tube whose arms are open to the atmosphere. Now water is poured into the U–tube from one arm, and light oil (?= 790 kg/m3) from the other. One arm contains 70–cm–high water, while the other arm contains both fluids with an oil–to–water height ratio of 6. Determine the height of each fluid in that arm.

Problem 34P The hydraulic lift in a car repair shop has an output diameter of 40 cm and is to lift cars up to 1800 kg. Determine the fluid gage pressure that must be maintained in the reservoir.

Freshwater and seawater flowing in parallel horizontal pipelines are connected to each other by a double U–tube manometer, as shown in Fig. P3–38. Determine the pressure difference between the two pipelines. Take the density of sea– water at that location to be \(\delta = 1035\ \text{kg/m}^3\). Can the air column be ignored in the analysis?

Problem 73P The two sides of a V-shaped water trough are hinged to each other at the bottom where they meet, as shown in Fig- P10-19, making an angle of 45° with the ground from both sides. Each side is 0.75 m wide, and the two parts are held together by a cable and turnbuckle placed every 6 m along? the length of the trough. Calculate the tension in each cable when the trough is filled to the rim.

Problem 74P Repeat Prob. 10-19 for the case of a partially filled trough with a water height of 0.4 m directly above the hinge. PROBLEM: The two sides of a V-shaped water trough are hinged to each other at the bottom where they meet, as shown in the figure, making an angle of 450 with the ground from both sides. Each side is 0.75 m wide, and the two parts are held together by a cable and turnbuckle placed every 6 m along the length of the trough. Calculate the tension in each cable when the trough is filled to the rim.

Problem 75P A retaining wall against a mud slide is to be constructed by placing 1.2–m–high and 0.25–m–wide rectangular concrete blocks (? = 2700 kg/m3) side by side, as shown in Fig. P3–80. The friction coefficient between the ground and the concrete blocks is f = 0.3, and the density of the mud is about 1800 kg/m3. There is concern that the concrete blocks may slide or tip over the lower left edge as the mud level rises. Determine the mud height at which (a) the blocks will overcome friction and start sliding and (b) the blocks will tip over.

A 1.2-m-diameter, 3-m-high sealed vertical cylinder is completely filled with gasoline whose density is \(740 \mathrm{~kg} / \mathrm{m}^{3}\). The tank is now rotated about its vertical axis at a rate of 70 \(\mathrm{rpm}\). Determine \((a)\) the difference between the pressures at the centers of the bottom and top surfaces and \((b)\) the difference between the pressures at the center and the edge of the bottom surface.

Problem 114P Reconsider Prob. 3–119. Using EES (or other) software, investigate the effect of rotational speed on the pressure difference between the center and the edge of the bottom surface of the cylinder. Let the rotational speed vary from 0 rpm to 500 rpm in increments of 50 rpm. Tabulate and plot your results.

Problem 115

Problem 149P The water in a 25-m-deep reservoir is kept inside by a 150-m-wide wall whose cross section is an equilateral triangle, as shown in Fig. P10-45. Determine (a) the total force (hydrostatic + atmospheric) acting on the inner surface of the wall and its line of action and (b) the magnitude of the horizontal component of this force. Take Patm = 100 kPa.

Problem 150P A U–tube contains water in the right arm, and another liquid in the left arm. It is observed that when the U–tube rotates at 50 rpm about an axis that is 15 cm from the right arm and 5 cm from the left arm, the liquid levels in both arms become the same, and the fluids meet at the axis of rotation. Determine the density of the fluid in the left arm.

Problem 151P A 1–m–diameter, 2–m–high vertical cylinder is completely filled with gasoline whose density is 740 kg/m3. The tank is now rotated about its Vertical axis at a rate of 90 rpm, while being accelerated upward at 5 m/s2. Determine (a) the difference between the pressures at the centers of the bottom and top surfaces and (b) the difference between the pressures at the center and the edge of the bottom surface.

Problem 1P Explain why some people experience nose bleeding and some others experience shortness of breath at high elevations.

Problem 2P Someone claims that the absolute pressure in a liquid of constant density doubles when the depth is doubled. Do you agree? Explain.

Problem 36P Repeat Prob. 3–38 by replacing the air with oil whose specific gravity is 0.72. PROBLEM: Freshwater and seawater flowing in parallel horizontal pipelines are connected to each other by a double U–tube manometer, as shown in Fig. P3–38. Determine the pressure difference between the two pipelines. Take the density of seawater at that location to be ? = 1035 kg/m3. Can the air column be ignored in the analysis? Fig P3-38

Problem 37P

Problem 38P

Problem 76P Repeat Prob. 3-80 for 0.4-m-wide concrete blocks. PROBLEM: A retaining wall against a mudslide is to be constructed by placing 1.2-m-high and 0.25-m-wide rectangular concrete block () side by side as shown in the figure. The friction coefficient between the ground and the concrete block is f = 0.4 and the density of the mud is about 1800 kg/m3. There is concern that the concrete blocks may slide or tip over the lower left edge as the mud level rises. Determine the mud height at which (a) the block will overcome friction and start sliding and (b) the blocks will tip over. Figure

Problem 78P Repeat Prob. 10-23 for a radius of 4 m for the gate.

Problem 116P A 3-m-diameter, 7-m-long cylindrical tank is completely filled with water. The tank is pulled by a truck on a level road with the 7-m-long axis being horizontal. Determine the pressure difference between the front and back ends of the tank along a horizontal line when the truck (a) accelerates at 3 m/s2 and (b) decelerates at 4 m/s2.

Problem 117P An air-conditioning system requires a 20-m-long section of 15-cm-diameter ductwork to be laid underwater. Determine the upward force the water will exert on the duct. Take the densities of air and water to be 1.3 kg/m3 and 1000 kg/m3, respectively.

Problem 118P Balloons are often filled with helium gas because it weighs only about one–seventh of what air weighs under identical conditions. The buoyancy force, which can be expressed as . will push the balloon upward. If the balloon has a diameter of 12 m and carries two people, 70 kg each, determine the acceleration of the balloon when it is first released. Assume the density of air is ? = 1.16 kg/m3, and neglect the weight of the ropes and the cage.

Problem 153P Reconsider Prob. 3–160. Using EES (or other) software, investigate the effect of acceleration on the slope of the free surface of water in the tank. Let the acceleration vary from 0 m/s2 to 15 m/s2 in increments of 1 m/s2. Tabulate and plot your results.

Problem 4P Express Pascal’s law, and give a real-world example of it.

Problem 3P A tiny steel cube is suspended in water by a string. If the lengths of the sides of the cube are very small, how would you compare the magnitudes of the pressures on the top, bottom, and side surfaces of the cube?

Consider two identical fans, one at sea level and the other on top of a high mountain, running at identical speeds. How would you compare (a) the volume flow rates and (b) the mass flow rates of these two fans?

The gage pressure of the air in the tank shown in Fig. P3-39 is measured to be 65 kPa. Determine the differential height h of the mercury column. FIGURE P3-39

Problem 40P Repeat Prob. 3–42 for a gage pressure of 45 kPa.

The top part of a water tank is divided into two compartments, as shown in Fig. P3–44. Now a fluid with an unknown density is poured into one side, and the water level rises a certain amount on the other side to compensate for this effect. Based on the final fluid heights shown on the figure, determine the density of the fluid added. Assume the liquid does not mix with water.

Problem 79P Consider a flat plate of thickness t, width w into the page, and length b submerged in water, as in Fig. P3–84. The depth of water from the surface to the center of the plate is H,and angle ? is defined relative to the center of the plate, (a) Generate an equation for the force F on the upper face of the plate as a function of (at most) h, b, t, w, g, ?, and ?. Ignore atmospheric pressure. In other words, calculate the force that is in addition to the force due to atmospheric pressure,(b) As a test of your equation, let H = 1.25 m, b = 1 m, t = 0.2 m, w = 1 m. g = 9.807 m/s2, ? = 998.3 kg/m3, and ? = 30°. If your equation is correct, you should get a force of 11.4 kN.

Problem 82P Consider a two–dimensional hinged cylindrical gate of radius R and width w into the page. The cylinder is resting at ground level with one quarter of its circumference submerged in water as in Fig. P3–87. The depth of water is h. (a) Generate an equation for the force F acting on the cylinder as a function of (at most) h, R, w, g,?, and L. Ignore atmospheric pressure since it acts on both sides of the cylinder. (b) As a test of your equation, let h = 5 m, R = 0.5 m, w = 1 m, g =9.807 m/s2, and ? = 998.3 kg/m3. If your equation is correct, you should get a force of 11.4 kN.

Problem 85P What is buoyant force? What causes it? What is the magnitude of the buoyant force acting on a submerged body whose volume is V? What are the direction and the line of action of the buoyant force?

Problem 119P Reconsider Prob. 3–125. Using EES (or other) software, investigate the effect of the number of people carried in the balloon on acceleration. Plot the acceleration against the number of people, and discuss the results.

Problem 120P Determine the maximum amount of load, in kg, the balloon described in Prob. 3–125 can carry.

Problem 121P The pressure in a steam boiler is given to be 90 kgf/cm2. Express this pressure in psi, kPa, atm, and bars.

Problem 155P [Reconsider Prob. 3–162. Using EES (or other) I software, investigate the effect of air pressure above water oh the cable force. Let this pressure vary from 0.5 MPa to 15 MPa. Plot the cable force versus the air pressure.

Problem 6P The piston of a vertical piston–cylinder device containing a gas has a mass of 85 kg and a crosssectional area of 0.04 m2 (Fig P3–7). The local atmospheric pressure is 95 kPa, and the gravitational acceleration is 9.81 m/s2.(a) Determine the pressure inside the cylinder. (b) If some heat is transferred to the gas and its volume is doubled, do you expect the pressure inside the cylinder to change?

Problem 7P A vacuum gage connected to a chamber reads 36 kPa at a location where the atmospheric pressure is 92 kPa. Determine the absolute pressure in the chamber.

Problem 8P The water in a tank is pressurized by air, and the pressure is measured by a multifluid manometer as shown in Fig. P3–10. Determine the gage pressure of air in the tank if h1= 0.2 m, h2 = 0.3 m, and h3 = 0.46 m. Take the densities of water, oil, and mercury to be 1000 kg/m3, 850 kg/m3, and 13,600 kg/m3, respectively.

The 500-kg load on the –hydraulic lift shown] in Fig. P3–45 is to be raised by pouring oil \(\left(\rho=780\mathrm{\ kg}/\mathrm{m}^3\right)\) into a thin tube. Determine how high h should be in order to begin to raise the weight.

Problem 43P Pressure is often given in terms of a liquid column and is expressed as “pressure head.” Express the standard atmospheric pressure in terms of (a) mercury (SG = 13.6). (b) water (SG = 1.0), and (c) glycerin (SG = 1.26) columns. Explain why we usually use mercury in manometers.

Problem 44P A simple experiment has long been used to demonstrate how negative pressure prevents water from being spilled out of an inverted glass. A glass that is fully filled by water and covered with a thin paper is inverted, as shown in Fig. P3–48. Determine the pressure at the bottom of the glass, and explain why water does not fall out.

Problem 86P Consider two identical spherical balls submerged in water at different depths. Will the buoyant forces acting on these two balls be the same or different? Explain.

Problem 87P Consider two 5-cm-diameter spherical balls—one made of aluminum, the other of iron—submerged in water. Will the buoyant forces acting on these two balls be the same or different? Explain.

Problem 88P Consider a 3-kg copper cube and a 3-kg copper ball submerged in a liquid. Will the buoyant forces acting on these two bodies be the same or different? Explain.

Problem 122P The basic barometer can be used as an altitude– measuring device in airplanes. The ground control reports a barometric reading of 753 mmHg while the pilot’s reading is 690 mmHg. Estimate the altitude of the plane from ground level if the average air density is 1.20 kg/m3.

Problem 123P The lower half of a 12–m–high cylindrical container is filled with water (? = 1000 kg/m3) and the upper half with oil that has a specific gravity of 0.85. Determine the pressure difference between the top and bottom of the cylinder.

Problem 124P A vertical, frictionless piston–cylinder device contains a gas at 500 kPa. The atmospheric pressure outside is 100 kPa, and the piston area is 30 cm2. Determine the mass of the piston.

Problem 9P Determine the atmospheric pressure at a location where the barometric reading is 735 mmHg. Take the density of mercury to be 13,600 kg/m3.

Problem 10P The gage pressure in a liquid at a depth of 3 m is read to be 28 kPa. Determine the gage pressure in the same liquid at a depth of 12 m.

Problem 11P The absolute presure to water at a depth of 5 m is read to be 145 kPa. Determine (a) the local atmospheric pressure and (b) the absolute pressure at a depth of 5 m in a liquid whose specific gravity is 0.78 at the same location.

Two chambers with the same fluid at their base are separated by a 30–cm–diameter piston whose weight is 25 N, as shown in Fig. P3–49. Calculate the gage pressures in chambers A and B.

Problem 46P Consider a double–fluid manaometer attached to an air pipe show in Fig. P3–50. If the specific gravity of the one fluid is 13.55, determine the specific gravity of the other fluid for for the indicated absolute pressure of air. Take the atmospheric pressure to be 100 kPa.

The pressure difference between an oil pipe and water pipe is measured by a double–fluid manometer, as shown in Fig. P3–51. For the given fluid heights and specific gravities, calculate the pressure difference ?P = PB– PA.

Problem 89P Discuss the stability of (a) a submerged and (b) a floating body whose center of gravity is above the center of buoyancy.

Problem 90P The density of a liquid is to be determined by an old 1–cm–diameter cylindrical hydrometer whose division marks are completely wiped out. The hydrometer is first dropped in water, and the water level is marked. The hydrometer is then dropped into the other liquid, and it is observed that the mark for water has risen 0.6 cm above the liquid–air interface (Fig. P3–95). If the height of the original water mark is 13.6 cm, determine the density of the liquid.

Problem 125P A pressure cooker cooks a lot faster than an ordinary pan by maintaining a higher pressure and temperature inside. The lid of a pressure cooker is well sealed, and steam can escape only through an opening in the middle of the lid. A separate metal piece, the petcock, sits on top of this opening and prevents steam from escaping until the pressure force overcomes the weight of the petcock. The periodic escape of the steam in this manner prevents any potentially dangerous pressure buildup and keeps the pressure inside at a constant value. Determine the mass of the petcock of a pressure cooker whose operation pressure is 100 kPa gage and has an opening cross–sectional area of 4 mm2. Assume an atmospheric pressure of 101 kPa, and draw the free–body diagram of the petcock.

Problem 91P The volume and the average density of an irregularly shaped body are to be determined by using a spring scale. The body weighs 7200 N in air and 4790 N in water. Determine the volume and the density of the body. State your assumptions.

Problem 126P A glass tube is attached to a water pipe, as shown in Fig. P3–133. If the water pressure at the bottom of the tube is 115 kPa and the local atmospheric pressure is 98 kPa, determine how high the water will rise in the tube, in m. Assume g =9.8 m/s2 at that location and take the density of water to be 1000 kg/m3.

Problem 127P The average atmospheric pressure on earth is approximated as a function of altitude by the relation Patm= 101.325 (1 – 0.02256z)5.256, where Patm is the atmospheric pressure in kPa and z is the altitude in km with z = 0 at sea level. Determine the approximate atmospheric pressures at Atlanta (z = 306 m), Denver(z= 1610 m), Mexico City (z = 2309 m), and the top of Mount Everest (z = 8848 m).

Problem 12P Show that 1 kgf/cm2 14.223 psi

Problem 13P

Problem 14P Consider a 55 kg woman who has a total foot imprint area of 400 cm2. She wishes to walk on the snow, but the snow cannot withstand pressures greater than 0.5 kPa. determine the minimum size of the snowshoes needed (imprint area per shoe) to enable her to walk on the snow without sinking.

Problem 48P Consider the system shown in Fig. P3–52. If a change of 0.7 kPa in the pressure of air causes the brine–mercury interface in the right column to drop by 5 mm in the brine level in the right column while the pressure in the brine pipe remains constant, determine the ratio of A2/A1.

Problem 49P Two water tanks are connected to each other through a mercery manometer with inclined tubes, as shown in Fig. P3–53. If the pressure difference between the two tanks is 20 kPa, calculate a and ?.

Problem 50P A multifluid container is connected to a U–tube, as shown in Fig. P3–54. For the given specific gravities and fluid column heights, determine the gage pressure at A. Also determine the height of a mercury column that would create the same pressure at A.

Problem 93P It is estimated that 90 percent of an iceberg’s volume is below the surface, while only 10 percent is visible above the surface. For seawater with a density of 1025 kg/ml3 estimate the density of the iceberg.

Problem 93P It is estimated that 90 percent of an iceberg’s volume is below the surface, while only 10 percent is visible above the surface. For seawater with a density of 1025 kg/ml3 estimate the density of the iceberg.

Problem 94P A 170-kg granite rock (? = 2700 kg/m3) is dropped into a lake. A man dives in and tries to lift the rock. Determine how much force the man needs to apply to lift it from the bottom of the lake. Do you think he can do it?

Problem 128P When measuring small pressure differences with a manometer, often one arm of the manometer is inclined to improve the accuracy of reading. (The pressure difference is still proportional to the vertical distance and not the actual length of the fluid along the tube.) The air pressure in a circular duct is to be measured using a manometer whose open arm is inclined 35° from the horizontal, as shown in Fig. P3–135. The density of the liquid in the manometer is 0.81 kg/L, and the vertical distance between the fluid levels in the two arms of the manometer is 8 cm. Determine the gage pressure of air in the duct and the length of the fluid column in the inclined arm

Problem 129P

Problem 130P A cylindrical container whose weight is 65 N is inverted and pressed into the water, as shown in Fig. P3–137. Determine the differential height h of the manometer and the force F needed to hold the container at the position shown.

Problem 15P A vacuum gage connected to a lank reads 30 kPa at a location where the barometric reading is 755 mmHg. Determine the absolute pressure in the tank. Take ?Hg = 13,590 kg/m3.

Problem 16P A pressure gage connected to a tank reads 500 kPa at a location where the atmospheric pressure is 94 kPa. Determine the absolute pressure in the tank.

Water from a reservoir is raised in a vertical tube of internal diameter D = 30 cm under the influence of the pulling force F of a piston. Determine the force needed to raise the water to a height of h = 1.5 m above the free surface. What would your response be for h = 3 m? Also, taking the atmospheric pressure to be 96 kPa, plot the absolute water pressure at the piston face as h varies from 0 to 3 m.

Problem 51P Consider a hydraulic jade being used in a car repair shop, as in Fig. P3–55. The pistons have an area of A1 = 1 cm2 and A2 = 0.04 m2. Hydraulic oil with a specific gravity of 0.870 is pumped in as the small piston on the left side is pushed up and down, slowly raising the larger piston on the right side. A car that weighs 20,000 N is to be jacked up. (a) At the beginning, when both pistons are at the same elevation (h = 0), calculate the force F1 in newtons required to hold the weight of the car.(b) Repeat the calculation after the car has been lifted two meters (h = 2 m). Compare and discuss.

Problem 56P Define the resultant hydrostatic force acting on a submerged surface, and the center of pressure.

Problem 22P

Problem 65P

Problem 105P