Please explain how did he get the result in the highlighted lines Water enters a

Question

Please explain how did he get the result in the highlighted lines

Water enters a house through a pipe 2.0 cm I.D. (1 cm radius) at an absolute pressure of 4xl05Pa. The pipe leading to the 2nd floor bathroom 5m above is 1.0 cm in diameter (0.5 cm radius). Velocity at the inlet is 4m/s. Find v and P at the bathroom. If the water is running in the bathroom: v2=A1/A2 v1 =( pi (0.01m)2/ pi (0.005m)2)(4m.s-1)=16m.s-1 p1 + 1/2pv1 2 + pgy = P2 + rho gy2 + 1/2 rho V2 2 P1 = P1 -1/2 rho (v2 2 - v1 2 ) - rho g(y2-y1) P2 = 2.3 times 105 Pa = 2.3atm If the water is turned off in the bathroom: P2 = P1 - 1/2 rho (0) - rho g(y2 - y1) rightarrow P2 = 3.5 times 105 Pa

Explanation / Answer

Given,
P1 = 4 x 105 pa , = 1000 kg /m3 , v1 = 4m/s , y1 = 0 , y2 = 5m.

when v2 = 16m/s

P2 = 4,00,000 - 0.5*1000*(256-16) - 1000*9.8*5 = 231000 = 2.31 x 105 Pa = 2.31 atm

when

v2 = v1 ,

P2 = 400000 -1000*9.8*5 = 400000 - 49000 = 351000 = 3.51 x 105 Pa

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