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4.2 Water enters a 4-in. square channel as shown at a velocity of 10 fps. The channel converges to a 2-in. square configuration as shown at the discharge end. The outlet section is cut at 30° to the vertical as shown, but the mean velocity of the discharging water remains horizontal. Find the exiting water’s average velocity and total rate of flow....
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4.3 The velocities in a circular duct of 20-in. diameter were measured as follows:
| Distance from center (in.) | Velocity (fps) |
| 0 | 7.5 |
| 3.16 | 7.10 |
| 4.45 | 6.75 |
| 5.48 | 6.42 |
| 6.33 | 6.15 |
| 7.07 | 5.81 |
| 7.75 | 5.47 |
| 8.37 | 5.10 |
| 8.94 | 4.50 |
| 9.49 | 3.82 |
| 10.00 | 2.40 |
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4.4 In the piston and cylinder arrangement shown below, the large piston has a velocity of 2 fps and an acceleration of 5 fps2. Determine the velocity and acceleration of the smaller piston....
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4.5 Using the symbol M for the mass in the control volume, show that equation (4-1) may be written...
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4.6 The velocity profile in circular pipe is given by υ = υmax(1 – r/R)1/7, where R is the radius of the pipe. Find the average velocity in the pipe in terms of υmax.
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4.7 Two very long parallel plates of length 2L are separated a distance b. The upper plate moves downward at a constant rate V. A fluid fills the space between the plates. Fluid is squeezed out between the plates. Determine the mass flow rate and maximum velocity under the following conditions:
a. The exit velocity is uniform....
b. The exit velocity is parabolic.
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4.8 The V-shaped tank has width w into the paper and is filled from the inlet pipe at volume flow Q. Derive expressions for (a) the rate of change dh/dt and (b) the time required for the surface to rise from h1 to h2....
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4.9 Water flows steadily through the piping junction, entering section 1 at 0.0013 m3/s. The average velocity at section 2 is 2.1 m/s. A portion of the flow is diverted through the showerhead, which contains 100 holes of 1-mm diameter. Assuming uniform shower flow, estimate the exit velocity from the showerhead jets....
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4.10 A vertical, cylindrical tank closed at the bottom is partially filled with an incompressible liquid. A cylindrical rod of diameter di (less than tank diameter, d0) is lowered into the liquid at a velocity V. Determine the average velocity of the fluid escaping between the rod and the tank walls (a) relative to the bottom of the tank and (b) relative to the advancing rod.
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4.11 Incompressible steady flow in the inlet between parallel plates is uniform, V0 = 8 cm/s, while downstream, the flow develops into the parabolic profile υx = az(z0 – z), where a is a constant. What is the maximum value of υx?...
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4.12 You are going to pressurize a tube using a mechanical pump. The standard bicycle tube is wrapped around a 24-in. diameter metal rim. The inflow to the pump is constant at 1 ft3/min. The density of the air leaving the pump is 0.075 lbm/ft3. The final inflated volume of a bicycle tube is 0.6 ft3. The density of air in the inflated tube is 0.4 lbm/ft3. The atmospheric pressure surrounding the system is 14.7 lbf/in2. Assuming that there are no leaks anywhere in the system, please calculate the time necessary to pressurize the tube if there initially is no air in the tube.
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4.13 A large tank of unknown total volume is initially filled with 6000 g of a 10% by mass sodium sulfate solution. Into this tank a 50% sodium sulfate solution is added at a rate of 40 g/min. At the single outlet to the tank flows a 20 g/L solution at a rate of 0.01667 L/sec. Please calculate (a) the total mass in the tank after 2 h and (b) the amount of sodium sulfate in the tank after 2 h.
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4.14 A cylindrical water tank is 4 feet high, with a 3-foot diameter, open to the atmosphere at the top is initially filled with water with a temperature of 60°F. The outlet at the bottom with a diameter of 0.5 in. is opened and the tank empties. The average velocity of the water exiting the tank is given by the equation ... where h is the height of the water in the tank measured from the center of the outlet port and g is the gravitational acceleration. Determine: (a) how long it will take for the water level in the tank to drop to 2 ft from the bottom, and (b) how long it will take to drain the entire tank.
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