To derive the hydrostatic equation, which of the following must be assumed? (Select all

Apply the grid method ( 1.5 inCh. 1) to each situation. a. If pressure is 6 inches of water (vacuum), what is gage pressure in kPa?b. lf the pressure is 180 kPa abs, what is the gage pressure in psi? c. If gage pressure is 0.4 bar, what is absolute pressure in psi? d. [fa person's blood pressure is 96 mm Hg, what is their blood pressure in kPa abs?

A 100 mm diameter sphere contains an ideal gas at 20C. :'-pply the grid method( 1.5 inCh. 1) to calculate the density in .:nits of kg/m3 . a. Gas is helium. Gage pressure is 20 in H20. b. Gas is methane. Vacuum pressure is 3 psi

For the questions below, assume standard atmospheric pressure. a. For a vacuum pressure of 30 kPa, what is the absolute pressure? Gage pressure? b. For a pressure of 13.8 psig, what is the pressure in psia? c. For a pressure of 200 kPa gage, what is the absolute pressure in kPa? d. Give the pressure 100 psfg in psfa.

The local atmospheric pressure is 99.0 kPa. A gage on m oxygen tank reads a pressure of 300 kPa gage. What is the ressure in the lank in kPa abs?

Using 3.1 and other resources, answer the following ~estions. Strive for depth, clarity, and accuracy while also ~ombining sketches, words, and equations in ways that enhance !e effectiveness of your communication. a. What are five important facts that engineers need to know about pressure? b. What are five common instances in which people use gage pressure? c. What are the most common units for pressure? d. Why is pressure defined using a derivative? e. How is pressure similar to shear stress? How does pressure differ from shear stress?

The Crosby gage tester shown in the figure is used calibrate or to test pressure gages. When the weights and the :- ton together weigh 140 N, the gage being tested indicates .:.00 kPa. If the piston diameter is 30 mm, what percentage of aror exists in the gage?

As shown, a mouse can use the mechanical advantage -ovided by a hydraulic machine to lift up an elephant. a. Derive an algebraic equation that gives the mechanical advantge of the hydraulic machine shown. Assume the pistons are friction less and massless. b. A mouse can have a mass of 25 g and an elephant a mass of7500 kg. Determine a value of D1 and D2 so that the mouse can support the elephant.

Find a parked automobile for which you have information on tire pressure and weight. Measure the area of tire contact with the pavement. Next, using the weight information and tire pressure, use engineering principles to calculate the contact area. Compare your measurement with your calculation and discuss.

To derive the hydrostatic equation, which of the following must be assumed? (Select all that are correct.) a. the specific weight is constant b. the fluid has no charged particles c. the fluid is at equilibrium

Consider Figure 3.8 on p. 67 of 3.2. a. Which fluid has the larger density? b. lf you graphed pressure as a function of z in these two layered liquids, in which fluid does the pressure change more with each incremental change in z?

Apply the grid method (1.5 in Ch. l) with the hydrostatic equation (tlp = 'Ytlz) to each of the following cases. a. Predict the pressure change t:.p in kPa for an elevation change tlz of I 0 ft in a fluid with a density of 90 lbm/ft 1 . b. Predict the pressure change in psf for a fluid with S = 0.8 and an elevation change of 22 m. c. Predict pressure change in inches of water for a fluid with a density of 1.2 kg/m3 and an elevation change of 1000 ft. d. Predict the elevation change in millimeters for a fluid with S = 13 that corresponds to a change in pressure of l/6atm.

Using 3.2 and other resources, answer the following questions. Strive for depth, clarity, and accuracy while also combining sketches, words, and equations in ways that enhance the effectiveness of your communication.a. What does hydrostatic mean? How do engineers identify whether a fluid is hydrostatic? b. What are the common forms on the hydrostatic equation? Are the forms equivalent or are they different? c. What is a datum? How do engineers establish a datum? d. What are the main ideas of Eq. (3.10) on p. 66 of 3.2? That is, what is the meaning of this equation? e. What assumptions need to be satisfied to apply the hydrostatic equation?

Apply the grid method to each situation. a. What is the change in air pressure in pascals between the floor and the ceiling of a room with walls that are 10 ft tall. b. A diver in the ocean (S = 1.03) records a pressure of 2.5 atm on her depth gage. How deep is she? c. A hiker starts a hike at an elevation where the air pressure is 940 mbar, and he ascends 1200 ft to a mountain summit. Assuming the density of air is constant, what is the pressure in mbar at the summit? d. Lake Pend Oreille, in northern Idaho, is one of the deepest lakes in the world, with a depth of 350 m in some locations. 'fl1is lake is used as a test facility for submarines. What is the maximum pressure that a submarine could experience in this lake? e. A 70 m tall standpipe (a standpipe is vertical pipe that is filled with water and open to the atmosphere) is used to supply water for fire fighting. What is the maximum pressure in the standpipe?

As shown, an air space above a long tube is pressurized to 50 kPa vacuum. Water (20C) from a reservoir fills the tube to a height h. If the pressure in the air space is changed to 25 kPa vacuum, will h increase or descrease and by how much? Assume atmospheric pressure is 100 kPa.

For the closed tank with Bourdon-tube gages tapped into it, what is the specific gravity of the oil and the pressure reading on gage C?

This manometer contains water at room temperature. The glass tube on the left has an inside diameter of 1 mm (d = 1.0 mm). The glass tube on the right is three times as large. For these conditions, the water surface level in the left tube will be (a) higher than the water surface level in the right tube, (b) equal to the water surface level in the right tube, or (c) less than the water surface level in the right tube. State your main reason or assumption for making your choice.

If a 200 N force f 1 is applied to the piston with the 4 ern diameter, what is the magnitude of the force F2 that can be resisted by the piston with the 10 em diameter? Neglect the weights of the pistons.

Regarding the hydraulic jack in Problem 3.18, which ideas were used to analyze the jack? (select all that apply)a. pressure = (force)(area) b. pressure increases linearly with depth in a hydrostatic fluid c. the pressure at the very bottom of the 4-cm chamber is larger than the pressure at the very bottom of the I 0-cm chamber d. when a body is stationary, the sum of forces on the object is zero e. when a body is stationary, the sum of moments on the object is zero f. pressure= (weight/volume)( change in elevation).

Water occupies the bottom 0.8 m of a cylindrical lank. . n lop of the water is 0.3 m of kerosene, which is open to the .:mosphere. If the temperature is 20C, what is the gage pressure u the bottom of the tank?

An engineer is designing a hydraulic lift with a capacity of .v tons. The moving parts of this lift weigh 1000 lbf. The lift itx>U!d raise the load to a height of 6 ft in 20 seconds. This will be J.:complished with a hydraulic pump that delivers fluid to a :Iinder. Hydraulic cylinders with a stroke of 72 inches are _ ailable with bore sizes from 2 to 8 inches. Hydraulic piston u.mps with an operating pressure range from 200 to 3000 psig ~available with pumping capacities of 5, 10, and 15 gallons per IDlJlute. Select a hydraulic pump size and a hydraulic cylinder .u that can be used for this application.

A tank with an attached manometer contains water at _""C. The atmospheric pressure is 100 kPa. There is a stopcock ocated 1 m from the surface of the water in the manometer. The opcock is closed, trapping the air in the manometer, and water added to the tank to the level of the stopcock. Find the increase 'l elevation of the water in the manometer assuming the air in ~ manometer is compressed isothermally

A tank is fitted with a manometer on the side, as shown. 1he liquid in the bottom of the tank and in the manometer has a specific gravity (S) of 3.0. The depth of tllis bottom liquid is 20 em. A 15 ern layer of water lies on top of the bottom liquid. Find the position of the liquid surface in the manometer .

As shown, a load acts on a piston of diameter D1 The piston rides on a reservoir of oil of depth h1 and specific gravity S. The reservoir is connected to a round tube of diameter D2 and oil rises in the tube to height h2. The oil in tl1e tube is open to atmosphere. Derive an equation for the height h2 in terms of the weight W of the load and other relevant variables. Neglect the weight of the piston.

As shown, a load of mass 5 kg is situated on a piston of diameter D1 = 120 mm. The piston rides on a reservoir of oil of depth ht = 42 mm and specifi c gravity S = 0.8. The reservoir is connected to a round tube of diameter D2 = 5 mm and oil rises in the tube to height h2. Find h2 Assume the oil in the tube is open to atmosphere and neglect the weight of the piston.

What is the maximum gage pressure in the odd tank shown in the figure? Where will the maximum pressure occur? What is the hydrostatic force acting on the top (CD) of the last chamber on the right-hand side of the tank? Assume T = 10C. Opent{> I atmosphere \ L\ I ! Plan VICW (View-) Open to atmosphere f """''"'

The steel pipe and steel chamber shown in the figure together weigh 600 lbf. What force will have to be exerted on the chamber by all the bolts to hold it in place? The dimension e is equal to 2.5 ft. Note: ll1ere is no bottom on the chamber-only a flange bolted to the floor.

What force must be exerted through the bolts to hold the dome in place? The metal dome and pipe weigh 6 kN. The dome has no bottom. Here e = 80 em and the specific weight of the water is -y = 9810 N/m3 .

The piston shown weighs I 0 lbf. In its initial position, the piston is restrained from moving to the bottom of the cylinder by means of the metal stop. Assuming there is neither friction nor leakage between piston and cylinder, what volume of oil (S = 0.85) would have to be added to the I in. tube to cause the piston to rise I in. from its initial position?

Consider an air bubble rising from the bottom of a lake. Neglecting surface tension, determine approximately what the ratio of the density of the air in the bubble will be at a depth of 34 ft to its density at a depth of 8 ft.

One means of determining the surface level of liquid in a :.ank is by discharging a small amount of air through a small -:~be, the end of which is submerged in the tank, and reading the ssure on the gage that is tapped into the tube. Then the level i the liquid surface in the tank can be calculated. If the pressure n the gage is IS kPa, what is the depth d of liquid in the tank?

For Fig. 3.9 on p. 70 of 3.2 that describes temperature "afiation with altitude, answer the following questions. a. Does the linear approximation relating temperature to altitude apply in the troposphere or the stratosphere? b. At approximately what altitude in the earth's atmosphere does the linear approximation for temperature variation fail?

The boiling point of water decreases with elevation because f the prcssun:: change. What is the boiling point of water at an d evation of 2000 m and at an elevation of 4000 m for standard mnospheric conditions?

From a depth of 10m in a lake to an elevation of 4000 min the atmosphere, plot the variation of absolute pressure. Assume that the lake water surface elevation is at mean sea level and .iSSume standard atmospheric conditions.

Assume that a woman must brea e a constant mass rate of air to maintain her metabolic processes. lf she inhales and exhales 16 times per minute at sea level, where the temperature is ; 9"F (lS0 C) and the pressure is 14.7 psia (101 kPa), what would "'U expect her rate of breathing at 18,000 ft (S486 m) to be? Use -tandard atmospheric conditions.

A pressure gage in an airplane indicates a pressure of 95 kPa at takeott: where the airport elevation is 1 km and the :em perature is l0C. If the standard lapse rate of S.87C/km is J.:>Sumed, at what elevation is the plane when a pressure of 7S kPa a read? What is the temperature for that condition?

Denver, Colorado, is called the "mile high" city. What are the pressure, temperature, and density of the air when standard mnospheric conditions prevail? Give your answer in traditional m d SI units.

The mean atmospheric pressure on the surface of Mars is 7 mbar, and the mean surface temperature is -63C. The atmosphere consists primarily of C02 (9S.3%) with small amounts of nitrogen and argon. The acceleration due to gravity on the surface is 3.72 m/s2 Data from probes entering the Martian atmosphere show that the temperature variation with altitude can be approximated as constant at -63C from the Martian surface to 14 km, and then a linear decrease with a lapse rate of I.SC/km up to 34 km. find the pressure at 8 km and 30 km altitude. Assume the atmosphere is pure carbon dioxide. Note that the temperature distribution in the atmosphere of Mars differs from that of Earth because the region of constant temperature is adjacent to the surface and the region of decreasing temperature starts at an altitude of 14 km.

Design a computer program that calculates the pressure and density for the U.S. standard atmosphere from 0 to 30 km altitude. Assume the temperature profiles are linear and are approximated by the following ranges, where z is the altitude in kilometers: 0- 13.72 km 13.7-16.8 km 16.8- 30 km T = 23.1 - S.87z (C) 'J' = - S7.5C T = - S7.5 + 1.387(z - 16.8tC

Match the following pressure-measuring devices with the correct name. The device names arc: barometer, Bourdon gage, piezometer, manometer, and pressure transducer. a. A vertical or U-shaped tube where changes in pressure are documented by changes in relative elevation of a liquid that is usually denser than the fluid in the system measured; can be used to measure vacuum . b. Typically contains a diaphragm, a sensing element, and conversion to an electric signal. c. A round face with a scale to measure needle deflection, where the needle is deflected by changes in extension of a coiled hollow tube. d. A vertical tube where a liquid rises in response to a positive gage pressure. e. An instrument used to measure atmospheric pressure; of various designs.

Which is the more correct way to describe the two summation (I) terms of the manometer equation, Eq (3.21) on p. 74 of 3.3? a. Add the downs and subtract the ups. b. Subtract the downs and add the ups.

Using the Internet and other resources, answer the following questions: a. What are three common types of manometers? For each type, make a sketch and give a brief description. b. How would you build a manometer from materials that are commonly available? Sketch your design concept.

As shown, gas at pressure Pg raises a column of liquid to a height h. The gage pressure in the gas is given by Pg = 'Yhquidh. Apply the grid method (p. 00) to each situation that follows. a. The manometer uses a liquid with S = 1.3. Calculate pressure in psia for h = 1 ft. b. The manometer uses mercury. Calculate the column rise in mm for a gage pressure of 0.25 atm. c. The liquid has a density of 30 lbm/ft1 . Calculate pressure in psfg for h = 4 inches. d. The liquid has a density of 800 kglm3 Calculate the gage pressure in bar for h = 3 m.

Is the gage pressure at the center of the pipe (a) negative, (b) zero, or (c) positive? Neglect surface tension effects and state your rationale.

Determine the gage pressure at the center of the pipe (point A) in pounds per square inch when the temperature is 70F with ht = 16in.andh2 = 2in.

Considering the effects of surface tension, estimate the gage pressure at the center of pipe A for h = 120 mm and T = 20C.

The ratio of container diameter to tube diameter is 8. When air in the container is at atmospheric pressure, the free surface in the tube is at position I. When the container is pressurized, the liquid in the tube moves 40 em up the tube from position 1 to "'OSition 2. What is the container pressure that causes this deflection? The liquid density is 1200 kg!m3

The ratio of container diameter to tube diameter is I 0. \'hen air in the container is at atmospheric pressure, the free -urface in the tube is at position I. When the container is :-ressurized, the liquid in the tube moves 3 ft up the tube from position I to position 2. What is the container pressure that causes this deflection? The specific weight of the liquid is 50 lbf/ft1 .

Determine the gage pressure at the center of pipe A in ;>ounds per square inch and in k.ilopascals.

A device for measuring the specific weight of a liquid -onsists of a U-tube manometer as shown. 1he manometer tube "'as an internal diameter of0.5 em and originally has water in it. ::.Xactly 2 em 1 of unknown liquid is then poured into one leg of "!e manometer, and a displacement of 5 em is measured between ~e surfaces as shown. What is the specific weight of the ~nk nown liquid?

Mercury is poured into the tube in the figure until the mercury occupies 375 nun of the tube's length. An equal volume of water is then poured into the left leg. Locate the water and mercury surfaces. Also determine the maximwn pressure in the tube.

Find the pressure at the center of pipe A. T = I 0C.

Determine (a) the difference in pressure and (b) the difference in piezometric head between points A and B. The elevations zA and z8 are 10m and II m, respectively, et = l m, and the manometer deflection f 2 is 50 em.

The deflection on the manometer is h meters when the pressure in the tank is 150 kPa absolute. If the absolute pressure in the tank is doubled, what will the deflection on the manometer be?

A vertical conduit is carrying oil (S = 0.95). A differential mercury manometer is tapped into the conduit at points A and R. Determine the difference in pressure between A and B when h = 3 in. What is the difference in piezometric head between A and 8?

A manometer is used to measure the pressure difference between points A and B in a pipe as shown. Water flows in the pipe, and the specific gravity of the manometer fluid is 2.8. The distances and manometer deflection are indicated on the figure. Find (a) the pressure differences PA - p8 , and (b) the difference in piezometric prcssure,pz,A - Pt.H Express both answers in kPa.

A novelty scale for measuring a person's weight by having the person stand on a piston connected to a water reservoir and stand pipe is shown in the diagram. The level of the water in the stand pipe is to be calibrated to yield the person's weight in pounds force. When the person stands on lhe scale, the height of the water in the stand pipe should be near eye level so the person can read it. There is a seal around the piston that prevents leaks but docs not cause a significant frictional force. The scale should function for people who weigh between 60 and 250 lbf and arc between 4 and 6 feet tall. Choose the piston size and standpipe diameter. Clearly stale the design features you considered. Indicate how you would calibrate the scale on the standpipe. Would the scale be linear?

Using 3.4 and other resources, answer the que ti ons below. Strive for depth, clarity, and accuracy while also combining sketches, words, and equations in ways that enhance the effectiveness of your communication. a. For hydrostatic conditions, what do typical pressure distributions on a panel look like? Sketch three examples that correspond to different situations.b. What is a center of pressure (CP)?What is a centroid of area? c. In Eq. (3.28) on p. 80 of *3.4, what does p mean? What factors influence the value of p? d. What is the relationship between the pressure distribution on a panel and the resultant force? e. How far is the CP from the centroid of area? What factors influence this distance?

Part 1. Consider the equation for the distance Oetween the CP and the centroid of a submerged panel Eq. (3.33) on p. 81 of 3.4). In that equation, y ep is a. the vertical distance from the water surface to the CP. b. the slant distance from the water surface to the CP. Part 2. Consider the figure shown. For case 1 as shown, the viewing .~indow on the front of a submersible exploration vehicle is at a depth of 11- For case 2, the submersible has moved deeper in :he ocean, to Yz- As a result of this increased overall depth of the submersible and its window, does the spacing between the CP and .:entroid (a) get larger, (b) stay the same, or (c) get smaller?

Which of these assumptions and/or limitations must be mown when using Eq. (3.33) on p. 81 of 3.4 for a submerged -urface or panel to calculate the distance between the centroid of ::he panel and the center of pressure of the hydrostatic force select all that apply): a. The equation only applies to a single fluid of constant density b. The pressure at the surface must be p = 0 gage c. The panel must be vertical d. The equation gives only the vertical location (as a slant distance) to the CP, not the lateral distance from the edge of the body

Two cylindrical tanks have bottom areas A and 4A ""eSpectively, and are filled with water to the depths shown. a. Which tank has the higher pressure at the bottom of the tank? b. Which tank has the greater force acting downward on the bottom circular surface?

What is the force acting on the gate of an irrigation .:.;tch if the ditch and gate are 4 ft wide, 4ft deep, and the ditch is .:ompetely full of water? There is no water on the other side of :.:.e gate. The weather has been hot for weeks, so the water is 70F.

Consider the two rectangular gates shown in the figure. They are both the same size, but gate A is held in place by a horizontal shaft through its midpoint and gate B is cantilevered to a shaft at its top. Now consider the torque T required to hold the gates in place as His increased. Choose the valid statement(s): (a) TA increases with H. (b) T8 increases with H. (c) TA does not change with H. (d) T8 does not change with H.

For gate A, choose the statements that are valid: (a) The hydrostatic force acting on the gate increases asH increases. (b) The distance between the CP on the gate and the centroid of the gate decreases as H increases. (c) The distance between the CP on the gate and the centroid of the gate remains constant asH increases. (d) 1he torque applied to the shaft to prevent the gate from turning must be increased as H increases. (e) The torque applied to the shaft to prevent the gate from turning remains constant as H increases.

As shown, a round viewing window of diameter D = 0.5 m is situated in a large tank of seawater (S = 1.03). The top of the window is 1.5 m below the water surface, and the window is angled at 60 with respect to the horizontal. Find the hydrostatic force acting on the window and locate the corresponding CP.

Find the force of the gate on the block. See sketch.

Assume that wet concrete (-y = 150 lbf/ft3) behaves as a liquid. Determine the force per unit foot of length exerted on the forms. If the forms are held in place as shown, with ties between vertical braces spaced every 2ft. what force is exerted on the bottom tie?

A rectangular gate is hinged at the water line, as shown. The gate is 4 ft high and 8 ft wide. The specific weight of water is 62.4lbf/ft 3 . Find the necessary force (in lbf) applied at the bottom of the gate to keep it dosed.

The gate shown is rectangular and has dimensions 6 m by 4 m. What is the reaction at point A? Neglect the weight of the gate.

Determine P necessary to just start opening the 2m- wide gate.

The square gate shown is eccentrically pivoted so that it automatically opens at a certain value of h. What is that value in terms of C?

This l 0 ft-diameter butterfly valve is used to .:ontrol the flow in a 10ft- diameter outlet pipe in a dam. In :he position shown, it is closed. The valve is supported by a 'lorizontal shaft through its center. What torque would have :o be applied to the shaft to hold the valve in the position ;.nown?

For the gate s own,a = 45 ,y d 1 = lm, an y2 = 4m. ~,~ill the gate fall or stay in position under the action of the -vdrostatic and gravity forces if the gate itself weighs 150 kN and is 1.0 m wide? Assume T = 10C. Use calculations to ~ify your answer.

Determine the hydrostatic force F on the triangular gate, -b.ich is hinged at the bottom edge and held by the reaction Rr the upper corner. Express Fin terms of -y, h, and W Also ;aermine the ratio Rrl F. Neglect the weight of the gate.

ln constructing dams, the concrete is poured in lifts of approximately 1.5 m ( y1 = 1.5 m). The forms for the face of the dan1 are reused from one lift to the next. The figure shows one such form, which is bolted to the already cured concrete. For the new pour, what moment will occur at the base of the form per meter of length (normal to the page)? Assume that concrete acts as a liquid when it is first poured and has a specific weight of 24 kN/m3 .

The plane rectangular gate can pivot about the support at B. For the conditions given, is it stable or unstable? Neglect the weight of the gate. Justify your answer with calculations.

Two hemispheric shells are perfectly sealed together, and the internal pressure is reduced to 25% of atmospheric pressure. The inner radius is 10.5 em, and the outer radius is 10.75 em. The seal is located halfway between the inner and outer radius. If the atmospheric pressure is 101.3 kPa, what force is required to pull the shells apart?

If exactly 20 bolts of 2.5 em diameter are needed to hold the air chamber together at AA as a result of the high pressure within, how many bolts will be needed at B-B? Here D = 40 em and d = 20cm.

For the plane rectangular gate (C X win ~ize), figure (a), what is the magnitude of the reaction at A in terms of -y,.. and the dimensions and w? For the cylindrical gate, figure (b), will the magnitude of the reaction at A be greater than, less than, or the same as that for the plane gate? Neglect the weight of the gates.

Water is held back by this radial gate. Does the resultant of the pressure forces acting on the gate pass above the pin, through the pin, or below the pin?

For the curved surface AB: Pm (center of curvature of gate) a. Determine the magnitude, direction, and line of action of the vertical component of hydrostatic force acting on the surface. Here f = 1 m. b. Determine the magnitude, direction, and line of action of the horizontal component of hydrostatic force acting on the surface. c. Determine the resultant hydrostatic force acting on the surface.

Determine the hydrostatic force acting on the radial gate if the gate is 40ft long (normal to the page). Show the line of action of the hydrostatic force acting on the gate.

This dome (hemisphere) is located below the water surface as shown. Determine the magnitude and sign of the force components needed to hold the dome in place and the line of action of the horizontal component of force. Here Yt = 1 m and y2 = 2 m. Assume T = 10C.

Consider the dome shown. This dome is 10ft in diameter, !Jut now the dome is not submerged. The water surface is at the lf'Vel of the center of curvature of the dome. For these comlitions, :!etennine the magnitude and direction of the resultant vdrostatic force acting on the dome.

Apply the grid method(* 1.5 inCh. I) to each situation -.elow. a. Determine the buoyant force in newtons on a basketball that is floating in a lake {10C). b. Determine the buoyant force in newtons on a 1 mm copper sphere that is immersed in kerosene. c. Determine the buoyant force in newtons on a 12 inchdiameter balloon. The balloon is filled with helium and situated in ambient air (20C).

Using 3.6 and other resources, answer the following i'lestions. Strive for depth, clarity, and accuracy while also .:r:>mbining sketches, words, and equations in ways that enhance ~e effectiveness of your commw1ication. a. Why learn about buoyancy? That is, what are important technical problems that involve buoyant forces? b. For a buoyant force, where is the CP? Where is the line of action? c. What is displaced volume? Why is it important? d. What is the relationship between pressure distribution and buoyant force?

Three spheres of the same diameter are submerged in the .l.llle body of water. One sphere is steel, one is a spherical .illoon filled with water, and one is a spherical balloon filled 'lth air. a. Which sphere has the largest buoyant force? b. If you move the steel sphere from a depth of 1 ft to 10 ft, what happens to the magnitude of the buoyant force acting on that sphere? c. Tf all 3 spheres are released from a cage at a depth of I m, what happens to the 3 spheres, and why?

As shown, a uniform-diameter rod is weighted at one end and is floating in a liquid. The liquid (a) is lighter than water, (b) must he water, or {c) is heavier than water. Show your work.

An 800 ft ship has a displacement of 35,000 tons, and the area defined hy the waterline is 38,000 ft2 Will the ship take more or less draft when steaming from salt water to fresh water? How much will it settle or rise?

A submerged spherical steel buoy that is 1.2 m in diameter and weighs 1200 N is to be anchored in salt water 20 m below the surface. Find the weight of scrap iron that should be sealed inside the buoy in order that the force on its anchor chain will not exceed 4.5 kN.

A buoy is designed with a hemispherical bottom and conical top as shown in the figure. The diameter of the hemisphere is 1 m, and the half angle of the cone is 30. The buoy has a mass of 460 kg. Find the location of the water line on the buoy floating in sea water {p = 1010 kg/mJ).

As shown, a cube (L = 60 mm) suspended in carbon tetrad or ide is exactly balanced by an object of mass m1 = 700 g. Find the mass m2 of the cube.

A block of material of unknown volume is submerged in water and found to weigh 300 N (in water). The same block weighs 700 N in air. Determine the specific weight and volume of the material

A I ft- diameter cylindrical Lank is filled with water to a depth of 2 ft. A cylinder of wood 5 in. in diameter and 2.5 in. long is set afloat on the water. 'I he weight of the wood cylinder is 21bf. Determine the change (if any) in the depth of the water in the tank.

A 90 inverted cone contains water as shown. The volume of the water in the cone is given by V = ('1T/3)h3 The original depth of the water is 10 em. A block with a volume of 200 cm3 and a specific gravity of 0.6 is floated in the water. What will be the change (in em) in water surface height in the cone?

The oating platform shown is supported at each corner by a hollow scaled cylinder l m in diameter. The platform itself weighs 30 kN in air, and each cylinder weighs 1.0 kN per meter of length. What total cylinder length L is required for the platform to float 1 m above the water surface? Assume that the specific weight of the water (brackish) is 10,000 N/m3 The platform is square in plan view.

To what depth d will this rectangular block (with density 0. 75 times that of water) float in the two-liquid reservoir?

Determine the minimum volume of concrete (-y = 23.6 kN/m3) needed to keep the gate (I m wide) in a closed position, withe= 2m. Note the hinge at the bottom of the gate.

A cylindrical container 4ft high and 2ft in diameter holds water to a depth of 2 ft. How much does the level of the water in the tank change when a 5 lb block of ice is placed in the container? Is there any change in the water level in the tank when the block of ice melts? Does it depend on the specific gravity of the ice? Explain all the processes.

The partially submerged wood pole is attached to the wall by a hinge as shown. The pole is in equilibrium under the action of the weight and buoyant forces. Determine the density of the wood.

A balloon is to be used to carry meteorological mstruments to an elevation of 15,000 ft where the air pressure is S.l psi a. The balloon is to be filled with helium, and the material from which it is to be fabricated weighs O.Qllbf/ft2 If the mstruments weigh 8lbf, what diameter should the spherical balloon have?

A weather balloon is constructed of a flexible material such that the internal pressure of the balloon is always 10 kPa hlgher than the local atmospheric pressure. At sea level the diameter of the balloon is 1 m, and it is filled with helium. The oalloon material, structure, and instruments have a mass of 100 g. This does not include the mass of the helium. As the Oalloon rises, it will expand. The temperature of the helium is always equal to the local atmospheric temperature, so it decreases as the balloon gains altitude. Calculate the maximum .Uti tude of the balloon in a standard atmosphere.

The hydrometer shown weighs 0.015 N. If the stem sinks 6.0 em in oil (z = 6.0 em), what is the specific gravity of :he oil?

The hydrometer shown sinks 5.3 em (z = 5.3 em) in water (15C). The bulb displaces 1.0 cm3 ,and the stem area is 0.1 cm2 . Find the weight of the hydrometer.

A common commercial hydrometer for measuring the amount of antifreeze in the coolant system of an automobile engine consists of a chamber with differently colored balls. The system is calibrated to give the range of specific gravity by distinguishing between the balls that sink and those that float. The specific gravity of an ethylene glycol-water mixture varies from 1.012 to 1.065 for 10% to 50% by weight of ethylene glycol. Assume there are six balls, 1 em in diameter each, in the chamber. What should the weight of each ball be to provide a range of specific gravities between 1.01 and 1.06 with 0.01 intervals?

A hydrometer with the configuration shown has a bulb diameter of 2 em, a bulb length of 8 em, a stem diameter of 1 em, a length of 8 em, and a mass of 40 g. What is the range of specific gravities that can be measured with this hydrometer? (Hint: Liquid levels range between bottom and top of stem.)

A barge 20ft wide and 40ft long is loaded with rocks as shown. Assume that the center of gravity of the rocks and barge is located along the centerline at the top surface of the barge. If the rocks and the barge weigh 400,000 lbf, will the barge float upright or tip over?

A floating body has a square cross section with side was shown in the figure. The center of gravity is at the centroid of the cross section. Find the location of the water line, C/ w, where the body would be neutrally stable (GM = 0). If the body is floating in water, what would be the specific gravity of the body material?

A cylindrical block of wood I m in diameter and 1 m long has a specific weight of 7500 N/m3 . Will it float in water with its axis vertical?

Is the block in this figure stable floating in the position shown? Show your calculations.