A sealed water tank is 40 cm in diameterand 4.5 m tall. The water level in the tankis at 4m and the remainder of the tank hasair at 1 atmosphere. A valve at the bottomof the tank is opened and water is allowedto flow out. After a while, the water stopsflowing, but the tank isn't empty. Whydid it stop flowing? What is the waterlevel in the tank (m) and how much waterwas released (m3)?

Given,Diameter of tank = 40 cm = 0.4mHeight of tank = 4.5mWater level in the tank = 4mPressure of empty space in tank = 1 atmTo find -a) why water stop flowingb) water level in tankc) water releaseda) As water starts flowing volume of empty space in the tank increases while the pressure decreases and the quantity of air in tank remains same due to which suction pressure is induced in the tank which stops the flow.b) In order to calculate water level in the tank using ideal gas equation which contains gasP1V1 = P2V2P1 = 1 atmV1 = area * heightV1 = π/4 * ( 0.4 )2 * 0.5SimilarlyV2 = π/4 * ( 0.4 )2 * h2 On equating P and V values we getP2 = 1 atm * o.5/h2Pressure at the bottom of the tank = density*g*hPressure at the bottom of the tank = 9810*(4.5 - h2)At condition of equilibrium i.e no for no flow1 atm * 0.5/h2 + 9810 * ( 4.5 - h2 ) = atmospheric pressureAtmospheric pressure or 1 atm = 101325 Pa101325 * 0.5/h2 + 9810 * ( 4.5 - h2 ) = 101325On solving 0.5 + 0.0968h2(4.5 - h2) = h20.0968h22 + 0.5644h2 - 0.5 = 0On solving above quadratic equation, we geth2 = 0.780 mWater level in tank = 4.5 - 0.780 = 3.72 mc) water released = area * ( 4 - 3.72 ) water released = π/4 * (0.4)2 * (4-3.72) Water released = 0.0351 m3a) why water stop flowing - because of suction pressureb) water level in tank = 3.72 mc) water released = 0.0351 m3