A village maintains a large tank with an open top, containing water for emergenc

Question

A village maintains a large tank with an open top, containing water for emergencies. The water can drain from the tank through a hose of diameter 6.05 cm. The hose ends with a nozzle of diameter 2.15 cm. A rubber stopper is inserted into the nozzle. The water level in the tank is kept 7.50 m above the nozzle.

(a) Calculate the friction force exerted by the nozzle on the stopper.
N

(b) The stopper is removed. What mass of water flows from the nozzle in 2.00 h?
kg

(c) Calculate the gauge pressure of the flowing water in the hose just behind the nozzle.
Pa

Explanation / Answer

a) Friction= force of water behind the stopper= pressure*area

=hdg*area (d=density of fluid, here, 1000kg/m^3)

7.5*1000*9.8* pi*(0.0215)^2= 105 N approx

b) mass= d*volume (volume= area*velocity, velocity= (2gh)^0.5 by torricelli's law of efflux)

which give mass flow rate=d*area*(2gh)^0.5/time

plugging values, we get mass flow rate as 2.44*10^-3 kg/s

c) Applying Bernoulli's equation change in pressure= dgh+dv^2/2 =2dgh(velocity at top of tank is taken as 0)

1000( 9.8*7.5)2 =147000 N/m^2 so gauge pressure would be total pressure- atmospheric pressure which gives 4.7*10^4 Pa

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