Question

A cylindrical tank is being filled with water. The tank is initially empty but then water begins to flow into it at a rate of 62.00 kg/min. There is a small hole of radius r = 0.7000 cm at the bottom of the tank where water can escape. Because the flow rate of water leaving the hole is initially at a slower rate than water entering the tank, the water level rises. The average velocity of water leaving through the hole at the bottom of the tank is not constant and is a function of the height of the water level in the tank: v=J2gh Yout v where g is the gravitational constant of Earth, 9.81 m/s2. Additionally, the density of water at this temperature is 1.000 x 103 kg/m² - R- > What is the maximum height of the water level in the tank, if it is initially empty? Number h= m If the radius of the tank is R = 0.9500 m, how long will it take the tank to reach 90.0% of this water level? Number

Answer 1

A th = alt a bhY2 het h=0 2=0 h = 2.061m, L=1.44m. 412 - Z 2th dh=dz ch - 255 oz oh - 22 oz A2207 dt a- bz dz a-bz = dt t en (1- &x 1.44)-o' T-b/a) & A (-2) en (1-6x144) t= -24 din (1 - 2 x 1.44) - As ITR² = 7 (0.95)2 = 2.83385m2 as Yin = 1.033 x 133 m 2 b = Ao fig = 1782/2g b= 15 (61 x 10-2) ? |2x 9.81 = 6,8158104

6 putting values of A a, and 6 in Ear ita -2x 833.85 m [1 - BAS X70*1.44) it- - 2x 2.83385 6.8158267 1.033X163 4.4 it - 24907.94 se el rt 6.92 hour mas water tank line will qoy take 6.92 hour to reach of maximum treatis livell

cow Rb-r. - 1 = laghi - 0.7cm. m = 62 kg/min. P = 1000 leg/m3 are know that m=sain (62 13 ) = (1000 leg) lin Lin = 0.062 y = 1:033210) = fagh g = 9.81 m/s2 Doing Maturian Balonu - & zih an Input - output - accumulation & lin - Shout = d (Ah) 8 is Constant an- Jout - Adh A area of tank. Ian- yout It - Steady state. maximum height will achieve at at steady state oth = 0 From Ean lin-yout - o

② in = Ao Jagh 1.033x10 3 (082) 2X out - AOV Area of hale A √ 249.8184 1.033 X 10-3 (7782) = 1,033 *10-3 IT (0:7X10-212 12x9.8184 = 6.714 2x9.818h (6.71412 hs 2.29 m Ihrex. = 2.29m me & If R=0.95m t=? 2 when h= 0.90 max. y = 0.90* 2.29 h = 2.06/m From Ear In - Yout= ain - Ao fagh Adh = a dhe A dlh an- Ao /29h a = dt dit A dha at Ein- Roza tla zat. net ain = a do jag = b.