Fluid mechanics 2nd edition solution manual pdf download free

Seepage is assumed to occur beneath the concrete wall, producing a linear distribution of hydrostatic pressure as shown. Determine the resultant force on a 1-ft wide portion of the wall and its location, measured to the right and upward from point A. The storage tank contains oil and water acting at the depths shown.

Determine the resultant force that both of these liquids exert on the side ABC of the tank if the side has a width of 1. Also, determine the location of this resultant, measured from the top surface of the oil. Since the side of the tank has a constant width, then the intensities of the distributed loading at B and C, Fig. Resultant Force. The resultant force can be determined by adding the shaded triangular and rectangular areas in Fig.

The resultant force is therefore 1. As shown, each of these three parallel resultants acts through the centroid of its respective area.

The location of the resultant force is determined by equating the moment of the resultant above A, Fig. The uniform rectangular relief gate AB has a weight of lb and a width of 4 ft. Determine the minimum depth h of water within the container needed to open it. The gate is pinned at B and rests on a rubber seal at A. Write the moment equation of equilibrium about B, referring to Fig. Determine the critical height h of the water level that causes the concrete gravity dam to be on the verge of tipping over due to water pressure.

Hint: Work the problem using a 1-m width of the dam. Then the intensity of the distributed load at the base of the dam is. The resulting triangular distributed load is shown on the FBD of the dam, Fig. The dam will overturn about point A. Write the moment equation of equilibrium about point A by referring to Fig. Determine the smallest thickness b of the concrete gravity dam that will prevent the dam from overturning due to water pressure acting on the face of the dam.

The resultant force of the triangular distributed load shown on the FBD of the dam, Fig. Writing the moment equation of equilibrium about point O, Fig. The uniform control gate AB is pinned at A and rests on the smooth surface at B. If the gate has a mass of 8. The gate has a width of 1 m. Determine the critical height h of the water level before the concrete gravity dam starts to tip over.

Hint: Work the problem using a 1-ft width of the dam. Assume water also seeps under the base of the dam and produces a uniform pressure under the dam. Referring to the FBD of the dam, Fig. The gate is 2 ft wide and is pinned at A and held in place by a smooth latch bolt at B that exerts a force normal to the gate.

Determine this force caused by the water and the resultant force on the pin for equilibrium. This load can be subdivided into two parts. The resultant force of each part is. Considering the free-body diagram of the gate, Fig. The uniform rectangular relief gate AB has a weight of lb and a width of 2 ft. Determine the components of reaction at the pin B and the normal reaction at the smooth support A.

Thus, the intensities of the distributed load at B and A are. The tide gate opens automatically when the tide water at B subsides, allowing the marsh at A to drain. The gate has a width of 2 m. At what height h will the gate be on the verge of opening? Determine the horizontal reaction at the smooth stop C as a function of the depth h of the water level.

The plot of FC vs h is shown in Fig. FC kN Dy. The bin is used to store carbon tetrachloride, a cleaning agent for metal parts. If it is filled to the top, determine the magnitude of the resultant force this liquid exerts on each of the two side plates, AFEB and BEDC, and the location of the center of pressure on each plate, measured from BE. The location of the center of pressure measured from BE can be obtained by equating the sum of the moments of the forces in Figs.

Determine the resultant force that the water and oil together exert on the wall ABC. The wall has a width of 2 m. Also, determine the location of this resultant measured from the top of the tank. Since the wall has a constant width, the intensities of the distributed loading at B and C, Fig. The resultant force can be determined by adding the areas of the triangles and rectangle, Fig. Each of the force components measured from the top acts through the centroid of its respective area.

The location of the resultant force can be determined by equating the moment of the resultant force and the force components about A, by referring to Figs. Determine the critical height h of the water level that causes the concrete gravity dam to be on the verge of tipping over. The resultant forces of the triangular distributed load and uniform distributed load due to the pressure of seepage water shown on the FBD of the dam, Fig.

The pressure of the air at A within the closed tank is kPa. Determine the resultant force acting on the plates BC and CD caused by the water. The tank has a width of 1. The uniform plate, which is hinged at C, is used to control the level of the water at A to maintain its constant depth of 6 m. If the plate has a width of 1.

The seepage is on the verge of occurring when the gate is about to open. Write the moment equation of equilibrium about point C by referring to Fig.

What is the resultant force acting on the gate? When the gate is on the verge of opening, the normal force at A and B is zero as shown on the free-body diagram of the gate, Fig.

Use the formula method. Since the gate is circular in shape, it is convenient to compute the resultant force as follows. Summing the moments about point C requires that FR acts through C. The tapered settling tank is filled with oil. Determine the resultant force the oil exerts on the trapezoidal clean-out plate located at its end. How far from the oil surface does this force act on the plate?

Determine the resultant force the oil exerts on the trapezoidal cleanout plate located at its end. Use the integration method. Ethyl alcohol is pumped into the tank, which has the shape of a four-sided pyramid. When the tank is completely filled, determine the resultant force acting on each side, and its location measured from the top A along the side.

The geometry of the side wall of the tank is shown in Fig. In this case, it is convenient to calculate the resultant force as follows. The bent plate is 2 m wide and is pinned at A and rests on a smooth support at B. Determine the horizontal and vertical components of reaction at A and the vertical reaction at the smooth support B for equilibrium. The fluid is water. The horizontal loading on the plate is due to the pressure on the vertical projected area of the plate.

F3 and F4 are not in the FBD are equal to the weight of water contained in the respective shaded rectangular and triangular blocks, Fig. Write the force equation of equilibrium along the x axis. The tank is filled to its top with an industrial solvent, ethyl ether. Determine the resultant force acting on the plate ABC, and its location on the plate measured from the base AB of the tank.

With respect to x and y axes established, the equation of side AB of the plate, Fig. Thus, the area of the differential element shown shaded in Fig.

Thus, the resultant force acting on the entire plate is 12 ft. If the tank is filled with vegetable oil, determine the resultant force that the oil exerts on plate A, and its location.

The location of the center of pressure can be determined by equating the sum of the moments of the forces in Figs. If the tank is filled with vegetable oil, determine the resultant force that the oil exerts on plate B, and its location.

Since the plate is circular in shape, it is convenient to compute the resultant force as follows. With respect to x and y axes established, the equation of the circumference of the circular plate is y 2. Determine the resultant force acting on the triangular plate A and the location of the center of pressure, measured from the free water level in the tank.

Solve the problem using the formula method. With respect to x and y axes established, the equation of side CD of the plate, Fig. The area of the differential element shown shaded in Fig. Thus, the resultant force acting on the entire plate is 5m. The open wash tank is filled to its top with butyl alcohol, an industrial solvent.

Determine the magnitude of the resultant force on the end plate ABCD and the location of the center of pressure, measured from AB. The tank truck is filled to its top with water. Determine the magnitude of the resultant force on the elliptical back plate of the tank, and the location of the center of pressure measured from the top of the tank.

The tank truck is half filled with water. Determine the magnitude of the resultant force on the elliptical back plate of the tank, and the location of the center of pressure measured from the x axis. Thus, the moment of inertia of the half of ellipse about its centroidal x axis can be determined by using the parallel-axis theorem.

The trough is filled to its top with carbon disulfide. Determine the magnitude of the resultant force acting on the parabolic end plate, and the location of the center of pressure measured from the top.

Take rcd 2. The tank is filled to its top with lubricating oil. Determine the resultant force acting on the semicircular plate ABC, and its location on the plate measured from the base AC of the tank. The tank is filled with water. Determine the resultant force acting on the trapezoidal plate C and the location of the center of pressure, measured from the top of the tank.

Thus, the resultant force acting on the entire plate is. The gate has a width of 3 ft. Neglect its weight.

The intensities of the distributed load at C and B shown in Fig. The control gate the smooth surface at B. ACB is pinned at A and rests on If the counterweight C is lb, depth of water h in the reservoir open. The uniform plate, which is hinged at C, is used to control the level of the water at A to maintain its constant depth of 12 ft.

If the plate has a width of 8 ft and a weight of 50 lb, determine the minimum height h of the water at B so that seepage will not occur at D.

For seepage to occur, the reaction at D must be equal to zero. Referring to the FBD of the gate, Fig. The bent plate is 1. Determine the horizontal and vertical components of reaction at A and the vertical reaction at the smooth support B. The gate is 1. Determine the reactions at these supports due to the water pressure. The vertical force acting on the plate is equal to the weight of the water contained in the block shown shaded in Fig.

Water is confined in the vertical chamber, which is 2 m wide. Determine the resultant force it exerts on the arched roof AB. This shaded block can be subdivided into two parts as shown in Figs.

The block in Fig. From the geometry in Fig. When this happens, the pressure at the well head A becomes 25 MPa. What should be the density of the mud so that the pressure at A becomes zero? In , S. Riva-Rocci developed the prototype of the current sphygmomanometer, a device used to measure blood pressure. When it was worn as a cuff around the upper arm and inflated, the air pressure within the cuff was connected to a mercury manometer.

If the reading for the high or systolic pressure is mm and for the low or diastolic pressure is 80 mm, determine these pressures in psi and pascals. Oxygen in a tank has an absolute pressure of kPa.

Then substitute Eq. Integrate Eq. A heavy cylindrical glass is inverted and then placed down at the bottom of a 12—ft-deep swimming pool. Assume the air in the glass remains at the same temperature as the atmosphere. Hint: Account for the change in volume of air in the glass due to the pressure change. The mm-diameter container is filled to the top with glycerin, and a mm-diameter pipe is inserted within it to a depth of mm.

Determine the maximum volume of kerosene that can be poured into the pipe while causing the displaced glycerin to overflow, so the kerosene does not come out from the bottom end. How high h does the kerosene rise above the glycerin? The kerosene is required to heat the bottom of the tube as shown in Fig. A kerosene h C 0. Butyl carbitol, used in the production of plastics, is stored in a tank having the U-tube manometer.

If the U-tube is filled with mercury to level E, determine the pressure in the tank at point B. Note: Since 0. Determine the pressures at points A and B. The containers are filled with water. Determine the pressure at point C.

Determine the difference in pressure pB - pA between the centers A and B of the pipes, which are filled with water. The mercury in the inclined-tube manometer has the level shown. Water in the reservoir is used to control the water pressure in the pipe at A. Neglect the diameter of the pipe. If the water pressure in the pipe at A is to be 25 kPa, determine the required height h of water in the reservoir.

E Mercury in the pipe has the elevation shown. A solvent used for plastics manufacturing consists of cyclohexanol in pipe A and ethyl lactate in pipe B that are being transported to a mixing tank. Determine the pressure in pipe A if the pressure in pipe B is 15 psi. Neglect the diameter of the pipes. If the pressure in pipe A is 18 psi, determine the height h of the mercury in the manometer so that a pressure of 25 psi is developed in pipe B.

The inverted U-tube manometer is used to measure the difference in pressure between water flowing in the pipes at A and B. If the top segment is filled with air, and the water levels in each segment are as indicated, determine the pressure difference between A and B. Referring to Fig. Solve Prob. Oil 0. The two tanks A and B are connected using a manometer. Air is also trapped in line CD as shown. The micro-manometer is used to measure small differences in pressure. The reservoirs R and upper portion of the lower tubes are filled with a liquid having a specific A B A B h1 gL weight of gR, whereas the lower portion is filled with a liquid having a specific weight of gt, Fig.

When the liquid flows through the venturi meter, the levels of the liquids R R d d with respect to the original levels are shown in Fig. If h2 the cross-sectional area of each reservoir is AR and the cross-sectional area of the U-tube is At, determine the pressure difference pA - pB. The liquid in the venturi meter e has a specific weight of gL. The Morgan Company manufactures a micro- B manometer that works on the principles shown.

Here there A are two reservoirs filled with kerosene, each having a cross- 2 sectional area of mm2. The connecting tube has a cross- sectional area of 15 mm2 and contains mercury. Hint: Both h1 and h2 can be eliminated from the analysis. Determine the difference in pressure pA - pB between the centers A and B of the closed pipes, which are filled with kerosene.

The pipes at A and B contain oil and the inclined- tube manometer is filled with oil and mercury. Determine the pressure difference between A and B.

A 2— The vertical pipe segment has an inner diameter of mm and is capped at its end and suspended from the horizontal pipe as shown. If it is filled with water and the pressure at A is 80 kPa, determine the resultant force that 2 m must be resisted by the bolts at B in order to hold the flanges together. Neglect the weight of the pipe but not the water within it. Here, FB is the force that must be resisted by the bolt, Ww is the weight of the water in segment BC of the pipe, and PB is the resultant force of pressure acting on the cross section at B.

Nitrogen in the chamber is at a pressure of 60 psi. Determine the total force the bolts at joints A and B must resist to maintain the pressure. There is a cover plate at B having a diameter of 3 ft.

For the bolts at B, Fig. For the bolts at A, Fig. Seepage is assumed to occur beneath the concrete wall, producing a linear distribution of hydrostatic pressure as shown. Determine the resultant force on a 1-ft wide portion of the wall and its location, measured to the right and upward from point A. The storage tank contains oil and water acting at the depths shown.

Determine the resultant force that both of these liquids exert on the side ABC of the tank if the side has a width of 1.