Please explain how did he get the result in the highlighted lines Water enters a
ID: 2202998 • Letter: P
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 PaExplanation / 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