A pump is used to send oil (density 800 kg/s) through a hose the diameter of whi

Question

A pump is used to send oil (density 800 kg/s) through a hose the diameter of which is 5 times that of the nozzle through which the water exits. If the nozzle is 1m higher than the pump and the oil flows through the hose at 0.2 m/s, what is the gauge pressure of the oil in the pump? the answer is 18 kPa how do you solve this? Thank you

Explanation / Answer

Using continuety equation A1V1=A2V2 =>pi*(5D)^2*0.2/4 =pi*D^2*V2/4 =>V2= 5m/s Applying bernouli equation P1+(1/2)*rho*V1^2+rho*g*h1 = P2+(1/2)*rho*V2^2+rho*g*h2 h1=0 h2=1m rho=800 =>P1-P2 =800*(0.5*5^2 +g*1-0.5*0.2^2 =>P2-Patm = 18kPa hence gauge pressure = 18kPa

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