1 MECH 371 HW 1 0.H1 (10 Points) Suppose we want to do the drag test for a solid car model in a water tunnel instead of a wind tunnel. We want to keep the flow speeds the same. a) How should we scale the car size (up or down) compared to the car in the wind tunnel to make sure that the drag coefficients are the same? b) What will be the ratio of the drag force in the water to the drag force in the air? As fluid properties, use the values given in class. 0.H2 (10 Points) Consider a room that is 20 m long, with linear temperature distribution from one end to the other, with the temperature being 4 o C higher at the right end. The temperature in the room is increasing uniformly at the rate of 10.8 o C every hour. What is the rate of temperature change a sensor would measure, if it is moving at… a) 0.01 m/s from left to right b) 0.02 m/s from left to right d) 0.01 m/s from right to left e) 0.02 m/s from right to left 0.H3 (10 Points) Consider a hypothetical flow situation where the fluid has a linear density distribution over a depth of 40 m, with the density being 2 kg/m 3 less at the higher end of that distribution. The density everywhere is increasing uniformly at the rate of 0.12 kg/m 3 every minute. Determine in which cases the flow is incompressible and in which cases it is compressible. The flow speed is… a) 0.04 m/s upward b) 0.08 m/s upward c) 0.04 m/s downward d) 0.08 m/s downward 0.H4 (10 Points) Calculate the Mach number for the following flow conditions. a) A passenger car speeding at 100 mph. b) A Bugatti Veyron speeding at 268 mph. c) The prototype mag-lev bullet train running at 374 mph. d) A peregrine falcon flying at 388 km/h at an altitude of 1000 m. e) A bullet fired into water with a muzzle velocity of 370 m/s. 0.H5 (5 Points) Consider a cylindrical structure with diameter D and natural frequency f s . It is placed in a uniform flow with speed U, perpendicular to the flow direction. Assuming a Strouhal number of 0.2, obtain an expression for U that results in the vortex-shedding frequency f f to be equal to the structure's natural frequency.
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MECH 371 HW 1
0.H1 (10 Points) Suppose we want to do the drag test for a solid car model in a water tunnel instead of a wind tunnel. We want to keep the flow speeds the same. a) How should we scale the car size (up or down) compared to the car in the wind tunnel to make sure that the drag coefficients are the same? b) What will be the ratio of the drag force in the water to the drag force in the air? As fluid properties, use the values given in class. 0.H2 (10 Points) Consider a room that is 20 m long, with linear temperature distribution from one end to the other, with the temperature being 4 oC higher at the right end. The temperature in the room is increasing uniformly at the rate of 10.8 oC every hour. What is the rate of temperature change a sensor would measure, if it is moving at… a) 0.01 m/s from left to right b) 0.02 m/s from left to right d) 0.01 m/s from right to left e) 0.02 m/s from right to left 0.H3 (10 Points) Consider a hypothetical flow situation where the fluid has a linear density distribution over a depth of 40 m, with the density being 2 kg/m3 less at the higher end of that distribution. The density everywhere is increasing uniformly at the rate of 0.12 kg/m3 every minute. Determine in which cases the flow is incompressible and in which cases it is compressible. The flow speed is… a) 0.04 m/s upward b) 0.08 m/s upward c) 0.04 m/s downward d) 0.08 m/s downward 0.H4 (10 Points) Calculate the Mach number for the following flow conditions. a) A passenger car speeding at 100 mph. b) A Bugatti Veyron speeding at 268 mph. c) The prototype mag-lev bullet train running at 374 mph. d) A peregrine falcon flying at 388 km/h at an altitude of 1000 m. e) A bullet fired into water with a muzzle velocity of 370 m/s. 0.H5 (5 Points) Consider a cylindrical structure with diameter D and natural frequency fs. It is placed in a uniform flow with speed U, perpendicular to the flow direction. Assuming a Strouhal number of 0.2, obtain an expression for U that results in the vortex-shedding frequency ff to be equal to the structure's natural frequency.
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MECH 371 HW 2
2.6 (5 Points)
2.22 (15 Points)
2.23 (15 Points)
2.30 (10 Points)
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MECH 371 HW 3
2.H1 (5 Points)
The tank of water accelerates to the right with the water in rigid-body motion. Calculate the acceleration that generates the configuration defined by the water heights hL and hR and the length L.
2.59 (10 Points)
2.52U (20 Points)
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MECH 371 HW 4 (Page 1 of 2)
2.80 (15 Points)
3.4 (15 Points) A suction device is arranged as shown. Find the volumetric flow rate (in ft3/s) through the main pipe at the instant at which the suction will begin. Assume incompressible and inviscid fluid and uniform atmospheric pressure.
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MECH 371 HW 4 (Page 2 of 2)
3.H1 (10 Points)
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MECH 371 HW 5
4.H1 (10 Points) In Example 4.A2… Find the value of V for which the force acting on the moving block is 1/4, 1/2, 2, and 4 times the force acting on a nonmoving block. 4.H2 (15 Points) Redo Example 4.A2 with the following modification: the inlet is the lower channel and the outlet is the upper channel, inclined at an angle θ with the horizontal as shown in the figure below. All other conditions in Example 4.A2 (including all the assumptions) remain the same.
4.H3 (15 Points) In Example 4.A3… At t = 0, instead of assuming V = 0, assume V = –U/4 (i.e., the block is moving backward at 1/4 of the absolute flow velocity at the inlet). Determine the time when the block reverses direction and starts moving forward.
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MECH 371 HW 6
5.H1 (10 Points) You are doing a flow computation for the aerodynamics of a car at 96 km/h. The car is 2 m wide. Assume that the air density and viscosity are the values given in class. You set the computational values of the density, car speed and car width to 1.0, 8 and 1. a) What do you need to use for the computational value of the viscosity? b) As the computational value of your time-step size, you are using 0.00125. You are asked to compute for a physical duration of 4 s. How many time steps do you need to compute? After the computation is complete… c) By what factor do you multiply the computational value of the pressure to recover the physical value of the pressure? d) By what factor do you multiply the computational value of the drag force to recover the physical value of the drag force? 5.H2 (15 Points) The diameter and density of a standard billiard ball are 5.715 cm and 1700 kg/m3. a) Find its terminal speed in water. Assume that water density and viscosity are the values given in class. For gravity, use g = 9.81 m/s2. Assume CD = 0.4. Do not neglect the buoyancy. b) Calculate the Reynolds number and determine if CD = 0.4 was a good or bad guess. c) Repeat a) and b) for a steel ball (density = 8050 kg/m3). 5.H3 (10 Points) A straight segment of an underwater cable (diameter 2 cm) is seeing a uniform flow stream of 0.4 m/s. With the x axis aligned with the flow direction, and with the z axis being vertical, the cable segment is in the x-z plane and inclined at 60o with the z axis. Assuming that the Reynolds number and the fluid mechanics force acting on the cable are determined only by the component of the flow velocity perpendicular to the cable, find the fluid mechanics force per unit length of the cable. Assume that water density and viscosity are the values given in class.
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MECH 371 HW 7
7.H1 (15 Points) Consider a pipe segment with length 2 m and diameter 2 cm, inclined at 30o with the horizontal. The pipe is carrying water. What pressure difference along the pipe segment do we need to have a flow rate of U = 5 cm/s? Use g = 9.81 m/s2. Assume that water density and viscosity are the values given in class. 7.H2 (15 Points) A pipe segment has length 1 m, diameter 4 cm, and relative roughness 5x10–4. The pipe is inclined at 60o with the horizontal and carrying water. What flow rate U do we get if the pressure difference along the pipe segment is 1.4433x104 Pa? Use g = 9.81 m/s2. Assume that water density and viscosity are the values given in class.
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