5.60 Two pipes, A and B, are connected to an open water tank. The water is entering the bottom of the tank from pipe A at 10 cfm. The water level in the tank is rising at 1.0 in. min, and the surface area of the tank is 80 ft 2 . Calculate the discharge in a second pipe, pipe B, that is also connected to the bottom of the tank. Is the flow entering or leaving the tank from pipe B ? 5.61 Is the tank in the figure filling or emptying ? At what rate is the water level rising or falling in the tank ? 5.62 Given: Flow velocities as shown in the figure and water sur- face elevation (as shown) at t 0 s . At the end of 22 s, will the water surface in the tank be rising or falling, and at what speed ? 5.63 A lake with no outlet is fed by a river with a constant flow of 1200 ft 3 s. Water evaporates from the surface at a constant rate of 13 ft 3 s per square mile surface area. The area varies with depth h (feet) as A (square miles) 4.5 5.5 h. What is the equilibrium depth of the lake ? Below what river discharge will the lake dry up ? 5.64 A stationary nozzle discharges water against a plate moving toward the nozzle at half the jet velocity. When the discharge from the nozzle is 5 cfs, at what rate will the plate deflect water ? 5.65 An open tank has a constant inflow of 20 ft 3 s. A 1.0 ft– diameter drain provides a variable outflow velocity V out equal to What is the equilibrium height h eq of the liquid in the tank ? 5.66 Assuming that complete mixing occurs between the two in- flows before the mixture discharges from the pipe at C , find the mass rate of flow, the velocity, and the specific gravity of the mixture in the pipe at C. 5.67 Oxygen and methane are mixed at 250 kPa absolute pres- sure and 100°C. The velocity of the gases into the mixer is 5 m s. The density of the gas leaving the mixer is 2.2 kg m 3 . Determine the exit velocity of the gas mixture. PROBLEM 5.58 PROBLEM 5.59 PROBLEM 5.61 2 m diameter V = 6 m/s V = ? 4 m/s 4 m diameter A B C 2 = 1.5 kg/m 3 ρ 1 = 2.0 kg/m 3 V 1 = 15 m/s ρ 1.2 m diameter 60 cm diameter 2 1 / 3 in diameter 4 in diameter 6 in diameter V = 10 ft/s V = 7 ft/s V = 4 ft/s 6 ft diameter Water / / + PROBLEM 5.62 PROBLEM 5.66 PROBLEM 5.67 Tank 12 in diameter Water 12 in diameter 6 in diameter 2 ft/s 1 ft/s 10 ft 2 ft diameter / 2 gh ( ) ft s / . Diameter = 6 in Closed tank A B C Diameter = 6 in Diameter = 4 in Q = 3 cfs S = 0.95 Q = 1 cfs S = 0.85 / / A = 3 cm 2 CH 4 A = 1 cm 2 A = 3 cm 2 O 2
156 CONTROL VOLUME APPROACH AND CONTINUITY EQUATION 5.68 A pipe with a series of holes as shown in the figure is used in many engineering systems to distribute gas into a system. The volume flow rate through each hole depends on the pres- sure difference across the hole and is given by where A o is the area of the hole, is the pressure difference across the hole and is the density of the gas in the pipe. If the pipe is sufficiently large, the pressure will be uniform along the pipe. A distribution pipe for air at 20 o C is 0.5 meters in diameter and 10 m long. The gage pressure in the pipe is 100 Pa. The pres- sure outside the pipe is atmospheric at 1 bar. The hole diameter is 2.5 cm and there are 50 holes per meter length of pipe. The pres- sure is constant in the pipe. Find the velocity of the air entering the pipe.
- Fall '18
- Fluid Dynamics, control surface