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Fluid Mechanics 2
A circular 2 m diameter gate is located on the sloping side of a swimming pool. The side of the pool is oriented 60 degrees relative to the horizontal bottom, and the center of the gate is located 3 m below the water surface. Determine the magnitude of the water force acting on the gate and the point through which it acts.
Water enters a cylindrical tank through two pipes at rates of 250 and 100 gal/min. If the level of the water in the tank remains constant, calculate the average velocity of the flow leaving the tank through an 8 in. inside diameter pipe.
The basic mechanism of the squirt gun shown at right consists of a trigger-driven piston/cylinder, a nozzle, and a tube connecting them. The cylinder diameter D=0.75 cm. The gun is used to shoot water (density p=998 kg/m^3) straight upwards to a height of 8.5 m. What force F is required on the trigger?
The wind blows through a 7 ft x 10 ft garage door opening with a speed of 5 ft/s as shown. Determine the average speeed, V, of the air through the two 3 ft x 4 ft openings in the windows.
For a certain incompressible flow field it is suggested that the velocity components are given by the equations: u=2xy , v=-x^2y , w=0 . Is this a physically possible flow field?
A water jet pump involves a jet cross-sectional area of .01 m^2, and a jet velocity of 30 m/s. The jet is surroundd by entrained water. the total cross-sectional area associated with the jet and entrained streams is .075 m^2. These two fluid streams leave the pump thoroughly mixed with an average velocity of 6 m/s through a cross-sectional area of .075 m^2. Determine the pumping rate (the entrained fluid flowrate) involved in liters/s.
Water flows through a converging/diverging pipe section. Inlet area A(1)=1.25 ft^2 while minimum area A(2)=.5 ft^2. Inlet pressure P(1)=75 lbf/in^2, while pressure at the minimum area P(2)=65 lbf/in^2. What is the volume flow rate through the pipe section?
Biomedical engineers wish to study the flow through an artificial heart valve, but the valve is too small for the flow measurement technique they want to use. The actual valve is circular, with a flow area A=3.00 cm^2. blood flows through the valve with volume flow rate Vdot=300 cm^3/s. The eingineers plan to do tests on an enlarged model valve with a flow area A=25 cm^2 using a clear mineral oil. they wish to keep the Reynolds number in the enlarged model valve the same as that in the actual valve. What volume flow rate should be used in the model valve?
Water enters a cylindrical tank through two pipes at rates of 250 and 100 gal/min. If the level of the water in the tank remains constant, calculate the average velocity of the flow leaving the tank through an 8 in. inside diameter pipe.
The basic mechanism of the squirt gun shown at right consists of a trigger-driven piston/cylinder, a nozzle, and a tube connecting them. The cylinder diameter D=0.75 cm. The gun is used to shoot water (density p=998 kg/m^3) straight upwards to a height of 8.5 m. What force F is required on the trigger?
The wind blows through a 7 ft x 10 ft garage door opening with a speed of 5 ft/s as shown. Determine the average speeed, V, of the air through the two 3 ft x 4 ft openings in the windows.
For a certain incompressible flow field it is suggested that the velocity components are given by the equations: u=2xy , v=-x^2y , w=0 . Is this a physically possible flow field?
A water jet pump involves a jet cross-sectional area of .01 m^2, and a jet velocity of 30 m/s. The jet is surroundd by entrained water. the total cross-sectional area associated with the jet and entrained streams is .075 m^2. These two fluid streams leave the pump thoroughly mixed with an average velocity of 6 m/s through a cross-sectional area of .075 m^2. Determine the pumping rate (the entrained fluid flowrate) involved in liters/s.
Water flows through a converging/diverging pipe section. Inlet area A(1)=1.25 ft^2 while minimum area A(2)=.5 ft^2. Inlet pressure P(1)=75 lbf/in^2, while pressure at the minimum area P(2)=65 lbf/in^2. What is the volume flow rate through the pipe section?
Biomedical engineers wish to study the flow through an artificial heart valve, but the valve is too small for the flow measurement technique they want to use. The actual valve is circular, with a flow area A=3.00 cm^2. blood flows through the valve with volume flow rate Vdot=300 cm^3/s. The eingineers plan to do tests on an enlarged model valve with a flow area A=25 cm^2 using a clear mineral oil. they wish to keep the Reynolds number in the enlarged model valve the same as that in the actual valve. What volume flow rate should be used in the model valve?
As shown in the figure, at the entrance to a 3-ft wide channel the velocity distribution is uniform with a velocty V. Further dwonstream the velocity profile is given by u=4y-2y^2, where u is in ft/s and y is in ft. Determine the value of V.
Air flows through a circular duct at mass flow rate m(dot)=1.750 kg/min. What is thhe minimum duct diameter that will definitely give laminar flow?
A thin solid sheet is held between an upper plate moving at 7.5 m/s and a lower stationary plate. The sheet is free to move horizontally. The space between the sheet and the upper plate is .2 mm thick and is filled with oil of viscosity .150 Ns/m^2. the space between the sheet and the lower plate is .05 mm thick and is filled with oil of viscosity .350 Ns/m^2. In steady state operation, what is the sheet's velocity?
Air at standard conditions enters the compressor shown in the figure at a rate of 10 ft^3/s. It leaves the tank through a 1.2 in diameter pipe with a density of .0035 slugs/ft^3 and a uniform speed of 700 ft/s. a) Determine the rate (slugs/s) at which the mass of the air in the tank is increasing or decreasing. b) Determine the average time rate of change of air densityh within the tank.
A tube partly filled with gasoline sits in a basin of water as shown in the figure at right. The gasoline floats on the water so that its surface is 3.5 inches above the surface of the water. How far below the surface of the water is the gasoline-water interface?
A domestic water heater contains 65 degree celcius water at 400 kPa gage. There is a small hole in the top of the tank. Neglecting friction: a) what is the height reached by the jet of water coming through the hole? b) What is the velocity of the jet immediately after it emerges from the hole?
Engineers plan to build a pipeline 1,000 km in length to transport water to a drought-stricken region. They wish to have a volume flow rate of 10 million gallons per day, and the maximum pipe diameter they can use is .5 m. The engineers do not wish to place a pump more frequently than every 20 km. The pipe material will be galvanized iron, roughness .15 mm. Determine: a) The average velocity of the water in the pipe and the Reynolds number, b) The pressure gradient along the pipe and the total pressure drop over its full length, c) The power of the pumps at each pumping station, assuming they are thermodynamically recersible.
A domestic water heater contains 150 degree F water at 60 lbf/in^2 gage. Neglecting friction, determine the height reached by a jet of water coming through a small hole in the top of the tank.
Air flows through a circular duct at mass flow rate m(dot)=1.750 kg/min. What is thhe minimum duct diameter that will definitely give laminar flow?
A thin solid sheet is held between an upper plate moving at 7.5 m/s and a lower stationary plate. The sheet is free to move horizontally. The space between the sheet and the upper plate is .2 mm thick and is filled with oil of viscosity .150 Ns/m^2. the space between the sheet and the lower plate is .05 mm thick and is filled with oil of viscosity .350 Ns/m^2. In steady state operation, what is the sheet's velocity?
Air at standard conditions enters the compressor shown in the figure at a rate of 10 ft^3/s. It leaves the tank through a 1.2 in diameter pipe with a density of .0035 slugs/ft^3 and a uniform speed of 700 ft/s. a) Determine the rate (slugs/s) at which the mass of the air in the tank is increasing or decreasing. b) Determine the average time rate of change of air densityh within the tank.
A tube partly filled with gasoline sits in a basin of water as shown in the figure at right. The gasoline floats on the water so that its surface is 3.5 inches above the surface of the water. How far below the surface of the water is the gasoline-water interface?
A domestic water heater contains 65 degree celcius water at 400 kPa gage. There is a small hole in the top of the tank. Neglecting friction: a) what is the height reached by the jet of water coming through the hole? b) What is the velocity of the jet immediately after it emerges from the hole?
Engineers plan to build a pipeline 1,000 km in length to transport water to a drought-stricken region. They wish to have a volume flow rate of 10 million gallons per day, and the maximum pipe diameter they can use is .5 m. The engineers do not wish to place a pump more frequently than every 20 km. The pipe material will be galvanized iron, roughness .15 mm. Determine: a) The average velocity of the water in the pipe and the Reynolds number, b) The pressure gradient along the pipe and the total pressure drop over its full length, c) The power of the pumps at each pumping station, assuming they are thermodynamically recersible.
A domestic water heater contains 150 degree F water at 60 lbf/in^2 gage. Neglecting friction, determine the height reached by a jet of water coming through a small hole in the top of the tank.
A 20 kg block and having dimensions of .2 m on each side slides down a 15 degree incline under its own weight. Between the bottom surface of the block and the incline is a film of oil .025 mm thick. The viscosity of the oil is .1 N-sec/m^2. Find the component of the weight of the block directed down the incline. Derive a symbolic algebraic expression for the viscous shear foce acting on the block (in terms of relevant variables) and determine the direction of this force. Derive a symbolic algebraic soluution for the velocity of the block (assuming constant velocity) as it slides down the inlcine.
The difference in density between hot air and cold air results in the chimney effect which draws air through many heating appliances. Suppose a fireplace has a chimney that is 15 m high. The chimney is filled with air at 300 degree C. the outdoor air temperature is 0 degrees C. At the top of the chimney, both the air in the chimney and the outside air are at 100 kPa. a) What is the density of the hot air leaving the chimney? b) What is the density of the cold air outside? c) Neglecting fluid friction and the change in density with elevation, what is the difference in pressure between the base of the chimney and the outdoors at the same elevation?
Water at 90 degrees F flows through a 1.00 inch inside diameter hose at a velocity of 10 ft/second. At the end of the hose is a nozzle with a .2 inch diameter opening. a) What is the velocity of the flow through the nozzle opening? b) What is the mass flow rate through the hose?
The figure at right shows the streamlines in a frictionless incompressible flow around a cylinder. Pressure is known at point X. Velocity and elevation are known everywhere. At which of points A-E can Bernoulli's equation be used to determine pressure?
A 200 foot long fire hose with an inside diameter of 2.5 inches delivers 250 gallons per minute of 70 degree F water. The average velocity of the water in the hose (for this flow rate) is approximately 16.3 ft/s. The inside of the hose is smooth. a) Is the flow of water inside the hose laminar or turbulent? b) What is the frictional pressure drop along the 200 ft length?
Consider the flow of water through a hypodermic needle. The inside diameter of the needle is .5 mm and its length is 75 mm. If 5 cc of water is injected over 8 seconds, estimate the average velocity of the water in the hypodermic and determine whether the flow within the needle is laminar or turbulent. Neglecting the entrance effects, determine the pressure drop through the hypodermic needle. Assuming the pressure at the exit of the needle is atmospheric, what is the gage pressure at the entrance to the needle?
The height of a fluid inside a tube or pipe can be used to measure the pressure at the base of the fluid column. An open standpipe contains 25 degrees C water, with the water surface 27 m above the ground. What is the gage pressure at the base of this water column? If the column were only 2 cm high, what would the gage pressure be?
Water is flowing in a pipe .15 m diameter. The pipe is horizontal, and flow is fully developed. The flow in the center of the pipe is turbulent, but the flow very close to the wall is laminar. A magnified velocity profile of the flow near the wall is whon at right. What is the shear stess at the wall? What is the pressure drop in a pipe 100 m long?
Two plates are separated by an oil film .01 mm thick. Oil viscosity is .1 N-sec/m^2. the upper plate is moving at 100 mm/s. The oil flow between the plates is laminar with a linear velocity profile. What is the shear stress at the surface of the lower plate?
The difference in density between hot air and cold air results in the chimney effect which draws air through many heating appliances. Suppose a fireplace has a chimney that is 15 m high. The chimney is filled with air at 300 degree C. the outdoor air temperature is 0 degrees C. At the top of the chimney, both the air in the chimney and the outside air are at 100 kPa. a) What is the density of the hot air leaving the chimney? b) What is the density of the cold air outside? c) Neglecting fluid friction and the change in density with elevation, what is the difference in pressure between the base of the chimney and the outdoors at the same elevation?
Water at 90 degrees F flows through a 1.00 inch inside diameter hose at a velocity of 10 ft/second. At the end of the hose is a nozzle with a .2 inch diameter opening. a) What is the velocity of the flow through the nozzle opening? b) What is the mass flow rate through the hose?
The figure at right shows the streamlines in a frictionless incompressible flow around a cylinder. Pressure is known at point X. Velocity and elevation are known everywhere. At which of points A-E can Bernoulli's equation be used to determine pressure?
A 200 foot long fire hose with an inside diameter of 2.5 inches delivers 250 gallons per minute of 70 degree F water. The average velocity of the water in the hose (for this flow rate) is approximately 16.3 ft/s. The inside of the hose is smooth. a) Is the flow of water inside the hose laminar or turbulent? b) What is the frictional pressure drop along the 200 ft length?
Consider the flow of water through a hypodermic needle. The inside diameter of the needle is .5 mm and its length is 75 mm. If 5 cc of water is injected over 8 seconds, estimate the average velocity of the water in the hypodermic and determine whether the flow within the needle is laminar or turbulent. Neglecting the entrance effects, determine the pressure drop through the hypodermic needle. Assuming the pressure at the exit of the needle is atmospheric, what is the gage pressure at the entrance to the needle?
The height of a fluid inside a tube or pipe can be used to measure the pressure at the base of the fluid column. An open standpipe contains 25 degrees C water, with the water surface 27 m above the ground. What is the gage pressure at the base of this water column? If the column were only 2 cm high, what would the gage pressure be?
Water is flowing in a pipe .15 m diameter. The pipe is horizontal, and flow is fully developed. The flow in the center of the pipe is turbulent, but the flow very close to the wall is laminar. A magnified velocity profile of the flow near the wall is whon at right. What is the shear stess at the wall? What is the pressure drop in a pipe 100 m long?
Two plates are separated by an oil film .01 mm thick. Oil viscosity is .1 N-sec/m^2. the upper plate is moving at 100 mm/s. The oil flow between the plates is laminar with a linear velocity profile. What is the shear stress at the surface of the lower plate?
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