Water at a gauge pressure of P = 5.8 atm at street level flows into an office bu
ID: 1286806 • Letter: W
Question
Water at a gauge pressure of P = 5.8 atm at street level flows into an office building at a speed of 0.90m/s through a pipe 5.6 cm in diameter. The pipe tapers down to 3.0 cm in diameter by the top floor, 16 m above (Figure 1) , where the faucet has been left open. Assume no branch pipes and ignore viscosity.
Part A
Calculate the flow velocity.
Express your answer to two significant figures and include the appropriate units.
Part B
Calculate the gauge pressure in the pipe on the top floor.
Water at a gauge pressure of P = 5.8 atm at street level flows into an office building at a speed of 0.90m/s through a pipe 5.6 cm in diameter. The pipe tapers down to 3.0 cm in diameter by the top floor, 16 m above (Figure 1) , where the faucet has been left open. Assume no branch pipes and ignore viscosity. no title provided Part A Calculate the flow velocity. Express your answer to two significant figures and include the appropriate units. Part B Calculate the gauge pressure in the pipe on the top floor.Explanation / Answer
a)
From equation of continuity
A1V1=A2V2
=>V2=(A1/A2)V1
since A=pi*d2/4
V2=(d1/d2)2V1=(5.6/3)2*0.9
V2=3.136 m/s=3.1 m/s (upto 2 significant figures)
b)
From bernoulli's theorem
P1+(1/2)pV12+pgh1=P2+(1/2)pV22+pgh2
P1+(1/2)*1000*0.92+1000*9.8*0=P2+(1/2)*1000*3.12+1000*9.8*16
P1-P2=1.612*105 pascals
1 atm=9.86923267*10-6 atm
P1-P2=1.612*105*(9.86923267*10-6)=1.6 atm
P2=P1-1.6 =5.8-1.6
P2=4.2 atm
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