Question

Q1: Consider the tank and water supply system as shown in Figure. The diameter of the supply pipe is D. = 40mm, and the average velocity leaving the supply pipe is V1 = 3 m/s. A shut- off valve is located at z = 0.7 m in the exit pipe, which has a diameter of D, = 30mm. The tank diameter is De = 0.7m. The density of the water is uniform at 998 kg/m. a. Find the time to fill the tank to Ho = 3m, assuming the tank is initially empty and the shut- off valve is closed. Neglect the volume associated with the short pipe connecting the tank to the shut-off valve. b. At the instant the water level reaches H= 3m, the shut-off valve is opened. The instantaneous average velocity of the outflow depends on the water depth above z and can be expressed by V2 = 0.85/9[H(t) – 2] where g is the acceleration due to gravity. Determine whether the tank continues to fill or begins to empty immediately after the valve is opened. c. Determine the steady-flow value of the water depth.

Answer 1

A umur walauopensojewssum Musea ETE SOLUTION S V EXRIVE 40mm m (01) SO DM3 1 015 3 = 2/10S (At) Suply pipe diamolie & Area of supply pipe = 7/4x0,² = 4000 x 100 m² Velocity leaving the supply = 3m/ Discharge through the supply (61) - A, 0,= 12X X10 -7 m3/ Tank diameter (Dt) = 0.7m → Hea of toonuk ettiamatex = 744 03 = 43.4 m2 @ Shut off value is closed Discharge leaving the tank = 0 Discharge entering the tank = P2 = 124 X10 mys the tank freed= At tho = 49 x x3 Qaxt LHS (Pout) Se 59160 Volume 3 of 147 km 400 400 VO Time taken a (+) = 147 N 400 IRkx10x t = 147 X alt = 306.25 seconds 400 (6) Shut-off value ů opened Area of 3225x10 m² 0.85 z yg (4c. diameter of sheet - off vales + 30mm ; shut off value=1/4x03 (ADE Instantaneous average velocity Hunough Value = NC (12) z=0.7m ig-9.81 2.66 √H(t)-0.7 m/s Discharge through the suppy value = AzV2 (022 = 1881.854 JH (- 07 X10-6 m3/s when the value is opened, 414) - Ho 3m 0.7 4,06 Q2 = 1881.854 x - 2.654 x 10° 0 m/

-3 3.77 x 10- m Pin = 128x10-4 I slo R - Pout = 2.854 x 10 3 m/ 3/5 Now, I Qin > Pout Thus, frank continues to give in immediately after the value ose opened. C. For stady-flow value of water depth Pin = Pout (.e.) whatever water enters unit time must flow out through shut-off valve per unit time. Pin - 0,= 127 810-4 m/s Pout = P2 = 1881.854 VHCE) - 0.7 x10-6 mo/8 P= P2 7 1881,854 x VACP) - 0.7 X10-6 | H(t) = 4.713 m MATE per 4 STAT Rnd = 120X10-4 Thus, sready state flow value of water depth = 4:713m