The chemisty building has pipes bringing water at a gauge pressure of 3.8 atm at

Question

The chemisty building has pipes bringing water at a gauge pressure of 3.8 atm at street level. Water flows into the pipe at a speed of 0.66m/s through a pipe which has a diameter of 5.1cm . By the top floor of the chemisty building, the pipe tapers down to a diameter of 3.0cm . The top floor of the chemisty building is 18 m above. An absent minded scientist left the faucet open at the top floor.

Part 1

What is the flow velocity in the pipe on the top floor? Pretend that there are no branch pipes and ignore viscosity.

part 2

What is the gauge pressure in the pipe at the top floor? Again, pretend that there are no branch pipes and ignore viscosity.

Explanation / Answer

part1)

A1 *v1 = A2 * v2

pi*d1^2/4 *v1 = pi*d2^2/4 *v2

d1^*v1 = d2^2*v2

5.1*5.1*0.66 = 3*3*v2

v2 = 1.9074 cm /s

part 2)

P2 = P1 - d*g*h

P2 = (3.8*1.013e5)-(1000*9.8*18) = 208540 Pa = 2.05 atm

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