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Fluid Mechanics
When an airplane is flying 200 mph at 5000 ft altitude in a standard atmosphere, the air velocity at a certain point on the wing is 273 mph relative to the airplane. What suction pressure is developed on the wing at that point? What is the pressure at the leading edge (a stagnation point) of the wing?
A loon is a diving bird equally at home flying in the air or water. What swimming velocity under water will produce a dynamic pressure equal to that when it flies in the air at 40 mph?
A fire hose nozzle has a diameter of 1 1/8 in. According to some fire codes, the nozzle must be capable of delivering at least 250 gal/min. If the nozzle is attached to a 3 in diameter hose, what pressure must sbe maintained just upstream of the nozzle to deliver this flowrate?
A jet of 25 degrees C water flows vertically from a garden hose nozzle with a velocity of 15 m/s. What is the maximum height that it can reach above the nozzle? If you place your hand in the stream just downstream of the nozzle exit what pressure would you feel acting against your hand?
A small bucket contains 25 degrees C water, .25 m deep. The bottom of the bucket is punctured with a .5 cm diameter hole, permitting water to squirt out. Neglecting viscous effects and assuming steady conditions, obtain a symbolic algebraic expression for the velocity of the water at the exit of the small hole. Calculate the magnitude of the velocity. Calculate the volume flowrate at the instant when the puncture first occurs.
Consider the flow of air through the venturi in an automobile carburetor. The volume flowrate through the venturi is .009 m^3/s. At the inlet to the venturi the cross sectional area is 5.0x10^-4 m^2, the pressure is 100 kPa, and the temperature is 35 degrees C. At the throat of the venturi the flow area is reduced to 1.7x10^-4 m^2. Assuming that the air can be considered incompressible: What is the air velocity at the inlet and throat of the venturi? What is the gage pressure at the throat of the venturi?
As shown in the figure at right, a 1.00 cm diameter siphon is used to drain 25 degrees C water from a tank. Use the Bernoulli equation to determine the mass flowrate of the water. Assume the pressure at both the water surface and the siphon discharge is atmospheric.
Joe is developing a portable speedometer for power boats. The device, shown in the figure at right, consists of a 1-inch diameter ell-shaped transparent plastic tube with graduations on the vertical leg of the ell. Joe places the tube in the water pointed in the direction of the boat's motion, with the bottom leg of the ell 1.00 foot below the surface. Water rises in the vertical leg to a level of 3 feet above the surface. How fast is the boat moving?
A loon is a diving bird equally at home flying in the air or water. What swimming velocity under water will produce a dynamic pressure equal to that when it flies in the air at 40 mph?
A fire hose nozzle has a diameter of 1 1/8 in. According to some fire codes, the nozzle must be capable of delivering at least 250 gal/min. If the nozzle is attached to a 3 in diameter hose, what pressure must sbe maintained just upstream of the nozzle to deliver this flowrate?
A jet of 25 degrees C water flows vertically from a garden hose nozzle with a velocity of 15 m/s. What is the maximum height that it can reach above the nozzle? If you place your hand in the stream just downstream of the nozzle exit what pressure would you feel acting against your hand?
A small bucket contains 25 degrees C water, .25 m deep. The bottom of the bucket is punctured with a .5 cm diameter hole, permitting water to squirt out. Neglecting viscous effects and assuming steady conditions, obtain a symbolic algebraic expression for the velocity of the water at the exit of the small hole. Calculate the magnitude of the velocity. Calculate the volume flowrate at the instant when the puncture first occurs.
Consider the flow of air through the venturi in an automobile carburetor. The volume flowrate through the venturi is .009 m^3/s. At the inlet to the venturi the cross sectional area is 5.0x10^-4 m^2, the pressure is 100 kPa, and the temperature is 35 degrees C. At the throat of the venturi the flow area is reduced to 1.7x10^-4 m^2. Assuming that the air can be considered incompressible: What is the air velocity at the inlet and throat of the venturi? What is the gage pressure at the throat of the venturi?
As shown in the figure at right, a 1.00 cm diameter siphon is used to drain 25 degrees C water from a tank. Use the Bernoulli equation to determine the mass flowrate of the water. Assume the pressure at both the water surface and the siphon discharge is atmospheric.
Joe is developing a portable speedometer for power boats. The device, shown in the figure at right, consists of a 1-inch diameter ell-shaped transparent plastic tube with graduations on the vertical leg of the ell. Joe places the tube in the water pointed in the direction of the boat's motion, with the bottom leg of the ell 1.00 foot below the surface. Water rises in the vertical leg to a level of 3 feet above the surface. How fast is the boat moving?
To cool a given room it is necessary to supply 5 ft^3/s of atmospheric pressure, 60 degrees F air through an 8 in-diameter duct. Approximately how long is the entrance length in this duct?
For an object of a given size moving at a given velocity through a fluid, which fluid flow will have the larger Reynolds number, air or water?
The average velocity U of a fluid flowing through a passage is related to cross-sectional area (A) and volume flow rate (V dot) by the expression V dot=UA. Combine this expression, the formula for Reynolds number, and the formula for area of a circle to develop a symbolic algebraic expression for the Reynolds number of flow through a passage of cirrcular cross-section. Your expression should be in terms of diameter, volume flowrate, and fluid properties. A garden hose with an inside diameter of 5/8 inch is supplying water at a rate of 3 gallons per minute. What is the Reynolds number of the flow? Is the flow laminar or turbulent?
If the characteristic dimension of a typical skydiver is 1.5 ft and if the sky-diver is in free-fall at a velocity of 120 miles/hr, what is the Reynolds number of this flow? (Assume air at atmospheric pressure and 70 degrees F.)
If P is pressure, V is velocity, and rho is fluid density, what are the dimensions (in the MLT system) of P/p, PVp, and P/pV^2 ?
An important dimensionless parameter in certain types of fluid flow problems is the Froude number defined as V/(gl)^(1/2), where V is velocity, g the acceleration of gravity, and l a length. Determine the value of the Froude number for V=10 ft/s, g=32.2 ft/s^2, and l=2 ft. Recalculate the Froude number using SI units for V,G, and l.
The information on a can of pop indicates that the can contains 355 mL. The mass of a full can of pop is .369 kg while an empty can weighs .153 N. Determine the specific weight, density, and specific gravity of the pop and compare your results with the corresponding values for water at 20 degrees C. Express your results in SI units.
A sled slides along a thin horizontal layer of water between the ice and the runners. The horizontal force that the water puts on the runners is equal to 1.2 lb when the sled's speed is 50 ft/s. The total area of both runners in contact with the water is .08 ft^2, and the viscosity of the water is 3.5x10^-5 lb s/ft^2. Determine the thickness of the water layer under the runners. Assume a linear velocity distribution in the water layer.
For an object of a given size moving at a given velocity through a fluid, which fluid flow will have the larger Reynolds number, air or water?
The average velocity U of a fluid flowing through a passage is related to cross-sectional area (A) and volume flow rate (V dot) by the expression V dot=UA. Combine this expression, the formula for Reynolds number, and the formula for area of a circle to develop a symbolic algebraic expression for the Reynolds number of flow through a passage of cirrcular cross-section. Your expression should be in terms of diameter, volume flowrate, and fluid properties. A garden hose with an inside diameter of 5/8 inch is supplying water at a rate of 3 gallons per minute. What is the Reynolds number of the flow? Is the flow laminar or turbulent?
If the characteristic dimension of a typical skydiver is 1.5 ft and if the sky-diver is in free-fall at a velocity of 120 miles/hr, what is the Reynolds number of this flow? (Assume air at atmospheric pressure and 70 degrees F.)
If P is pressure, V is velocity, and rho is fluid density, what are the dimensions (in the MLT system) of P/p, PVp, and P/pV^2 ?
An important dimensionless parameter in certain types of fluid flow problems is the Froude number defined as V/(gl)^(1/2), where V is velocity, g the acceleration of gravity, and l a length. Determine the value of the Froude number for V=10 ft/s, g=32.2 ft/s^2, and l=2 ft. Recalculate the Froude number using SI units for V,G, and l.
The information on a can of pop indicates that the can contains 355 mL. The mass of a full can of pop is .369 kg while an empty can weighs .153 N. Determine the specific weight, density, and specific gravity of the pop and compare your results with the corresponding values for water at 20 degrees C. Express your results in SI units.
A sled slides along a thin horizontal layer of water between the ice and the runners. The horizontal force that the water puts on the runners is equal to 1.2 lb when the sled's speed is 50 ft/s. The total area of both runners in contact with the water is .08 ft^2, and the viscosity of the water is 3.5x10^-5 lb s/ft^2. Determine the thickness of the water layer under the runners. Assume a linear velocity distribution in the water layer.
The space between two 6 in long concentric cylinders is filled with glycerin (viscosity= 8.5x10^-3 lb s/ft^2). The inner cylinder has a radius of 3 in. and the gap width between cylinders in .1 in. Determine the torque and the power required to rotate the inner cylinder at 180 rev/min. The outer cylinder is fixed. Assume the velocity distribution in the gap to be linear.
Bourdon gages are commonly used to measure pressure. When such a gage is attached to the closed water tank in the figure to the right the gage reads 5 psi. What is the absolute air pressure in the tank? Assume standard atmospheric pressure of 14.7 psi.
On the suction side of a pump a Bourdon pressure gage reads 40 kPa vacuum. What is the corresponding absolute pressure if the local atmospheric pressure is 100 kPa (abs)?
Air flows steadily through a long pipe with a speed of u=50+.5x, where x is the distance along the pipe in feet, and u is in ft/s. Due to heat transfer into the pipe, the air temperature, T, within the pipe is T=300+10x degrees F. Determine the rate of change of the temperature of air particles as they flow past the section at x=5 ft.
A two-dimensional velocity field is given by u=1+y and v=1. Determine the equation of the streamline that passes through the origin. On a graph, plot this streamline.
Determine the acceleration field for a three-dimensional flow with velocity components u=-x, v=4x^2y^2, and w=x-y.
Water flows through the 2 m wide rectangular channel shown in the figure with a uniform velocity of 3 m/s. a) Directly integrate Reynolds equation with b=1 to determine the mass flowrate (kg/s) across section CD of the control volume. b) Repeat part (a) with b=1/p, where p is the density.
Water is squirted from a syringe with a speed of V=5 m/s by pushing in the plunger with a speed of V(p)=.03 m/s as shown in the figure. The surafce of the deforming control volume consists of the sides and end of the cylinder and the end of the plunger. The system consists of the water in the syringe at t=0 when the plunger is at section (1) as shown. Make a sketch to indicate the control surface and the system when t=.5 s.
The wind blows across a field with an approximate velocity profile as shown in the figure. Use Reynolds equation with the parameter V equal to the velocity to determine the momentum flowrate across the vertical surface A-B which is of unit depth into the paper.
Bourdon gages are commonly used to measure pressure. When such a gage is attached to the closed water tank in the figure to the right the gage reads 5 psi. What is the absolute air pressure in the tank? Assume standard atmospheric pressure of 14.7 psi.
On the suction side of a pump a Bourdon pressure gage reads 40 kPa vacuum. What is the corresponding absolute pressure if the local atmospheric pressure is 100 kPa (abs)?
Air flows steadily through a long pipe with a speed of u=50+.5x, where x is the distance along the pipe in feet, and u is in ft/s. Due to heat transfer into the pipe, the air temperature, T, within the pipe is T=300+10x degrees F. Determine the rate of change of the temperature of air particles as they flow past the section at x=5 ft.
A two-dimensional velocity field is given by u=1+y and v=1. Determine the equation of the streamline that passes through the origin. On a graph, plot this streamline.
Determine the acceleration field for a three-dimensional flow with velocity components u=-x, v=4x^2y^2, and w=x-y.
Water flows through the 2 m wide rectangular channel shown in the figure with a uniform velocity of 3 m/s. a) Directly integrate Reynolds equation with b=1 to determine the mass flowrate (kg/s) across section CD of the control volume. b) Repeat part (a) with b=1/p, where p is the density.
Water is squirted from a syringe with a speed of V=5 m/s by pushing in the plunger with a speed of V(p)=.03 m/s as shown in the figure. The surafce of the deforming control volume consists of the sides and end of the cylinder and the end of the plunger. The system consists of the water in the syringe at t=0 when the plunger is at section (1) as shown. Make a sketch to indicate the control surface and the system when t=.5 s.
The wind blows across a field with an approximate velocity profile as shown in the figure. Use Reynolds equation with the parameter V equal to the velocity to determine the momentum flowrate across the vertical surface A-B which is of unit depth into the paper.
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