Water at a gauge pressure of P = 3.6 atm at street level flows into an office bu

Question

Water at a gauge pressure of P = 3.6 atm at street level flows into an office building at a speed of 0.90m/sthrough a pipe 4.8 cm in diameter. The pipe tapers down to 2.0 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.

Express your answer to two significant figures and include the appropriate units.

vtop = Water at a gauge pressure of P = 3.6 atm at street level flows into an office building at a speed of 0.90m/sthrough a pipe 4.8 cm in diameter. The pipe tapers down to 2.0 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. vtop = Part B Calculate the gauge pressure in the pipe on the top floor. Express your answer to two significant figures and include the appropriate units. Pgaugetop =

Explanation / Answer

Let 1 be the position on the street and 2 on the top floor

v2 = v1*A1/A2 = 0.90*?*(0.024^2)/(?*(0.01^2)) = 5.184m/s

Now p1 + ?*g*y1 + 1/2*?*v1^2 = p2 + ?*g*y2 + 1/2*?*v2^2

So p2 = p1 + ?*g*(y1 - y2) + 1/2*?*(v1^2 - v2^2)

= 3.6*1.01x10^5Pa/atm + 1000*9.8*(0 - 16) + 1/2*1000*(0.90^2 - 5.2^2) = 1.93685x10^5 Pa

= 1.93685x10^5/ 1.01x10^5 = 1.9176atm

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