Fluids answers unformatted

Fluids answers unformatted
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A 1. tank is filled with seawater to a depth of 12 ft. If the specific gravity of seawater is 1.03 and the atmospheric pressure at this location is 14.8 psi, the absolute pressure (psi) at the bottom of the tank is most nearly A. 5.4 B. 20.2 C. 26.8 D. 27.2 Hint: Absolute pressure = gage pressure + atmospheric pressure where, gage pressure = zh and z = specific weight of seawater = SG x w Solution: z = 1.03 (62.4 lb/cu ft) = 64.27 lb/cu ft Gage pressure at the bottom of the tank = (12 ft) x (64.37 lb/cu ft) = 772.44 lb/sq ft = (772.44 lb/sq ft)/(144 sq in/sq ft) = 5.36 psi Absolute pressure = 14.8 psi + 5.36 psi= 20.16 psi Therefore, the key is (B). 2. An open tank contains brine to a depth of 2 m and a 3-m layer of oil on top of the brine. Density of brine is 1,030 kg/m3 and the density of oil is 880 kg/m3. The gage pressure (kPa) at the bottom of the tank is most nearly A. 4.7 B. 20.2 C. 25.6 D. 46.1 Hint: Pressure due to each layer of liquid = h where h is the height of the liquid layer and is the specific weight of the liquid. Solution: Since it is required to determine the gage pressure, pressure at the free surface = 0 Pressure due to the oil layer = (3 m) {(880 kg/m3)(9.81 m/s2)}/1,000= 25.9 kPa Pressure due to the brine layer= (2 m) {(1,030 kg/m3) (9.81 m/s2)}/1,000= 20.2 kPa Hence pressure at the bottom= 25.9 + 20.2 = 46.1 kP Note: 1 kg-ms2 = 1 N; 1 N/m2 = 1 Pa Therefore, the key is (D). 3 The figure shows two cylinders of diameter D and 2D, connected to each other and . containing an incompressible fluid. The two cylinders are fitted with leak-proof pistons of weight W1 and W2 as shown. Which of the following is a correct expression? A. W2 = W1/2 B. W2 = W1 C. W2 = 2 W1 D. W2 = 4 W1 Hint: The pressure is the same in both cylinders. Pressure = Weight/area Solution: Considering the weight W1, pressure Considering the weight W2, pressure Equating the two, Hence, W2 = 4 W1 Therefore, the key is (D). 4. The figure shows the relationship between shear stress and velocity gradient for two fluids, A and B. Which of the following is a true statement? A. Absolute viscosity of A is greater than that of B B. Absolute viscosity of A is less than that of B C. Kinematic viscosity of A is greater than that of B D. Kinematic viscosity of A is less than that of B Hint: By definition, absolute viscosity Thus, slope of the lines in the plot is absolute viscosity. Kinematic viscosity = absolute viscosity/density. Solution: Since the slope of the line for A is greater than that for B, viscosity of A is greater than that of B. Therefore, the key is (A). 5. A flat plate is sliding at a constant velocity of 5 m/s on a large horizontal table. A thin layer of oil (of absolute viscosity = 0.40 N-s/m2) separates the plat from the table. To limit the shear stress in the oil layer to 1 kPa, the thickness of the oil film (mm) should be most nearly A. 0.2 B. 1.6 C. 2.0 D. 3.5 Hint: By definition, absolute viscosity, where, velocity gradient = DU/d, DU = difference in velocity
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