## Water at a gauge pressure of 3.8 atm at street level flows into an office building at a speed of 0.78 m/s through a pipe 5.0 cm in diameter.

Question

Water at a gauge pressure of 3.8 atm at street level flows into an office building at a speed of 0.78 m/s through a pipe 5.0 cm in diameter. The pipe tapers down to 2.8 cm in diameter by the top floor, 16 m above, where the faucet has been left open.
Calculate the flow velocity and the gauge pressure in the pipe on the top floor. Assume no branch pipes and ignore viscosity.

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6 months 2021-07-17T09:14:00+00:00 2 Answers 29 views 0

The flow velocity is

The  gauge pressure is

Explanation:

The diagram for this question is shown on the first uploaded image

From the question we are told that

The gauge pressure

The speed of flow is

The diameter of the pipe is

The diameter at the top floor is

The the height from the ground is

So we are going to make some assumption

We would assume that the position on the street is A

and the position on the top floor is B

So from continuity equation the velocity of the flow in the street is

Where

is the area of the pipe at the base

So

and   i the area of the pipe at the top floor

substituting values

So

Applying Bernoulli’s equation

Since the pipe started from the floor

Here the is the density of water with value

Substituting values

Converting back to atm

= 2.49 m/s

= 2.19 atm

Explanation:

By using continuity equation:

= ($$v_1$$) / = ( = (5/2.8)² x 0.78 = 2.49 m/s

By using Bernoulli’s Equation:

+ ρg + ½ρ ( )²= + ρg + ½ρ( )²

[ ² – ²] /2  = ( )/ ρ + g()

(0.78²- 2.49²)/2 = ( )/ 1000 + (9.8 x 16)

-5.6= ( )/ 1000 + (156.8)

( ) = – 162400 Pa

= -162400,   = 3.8atm = 385035 Pa

= 385035-162400 = 222635 Pa ( gauge  pressure)

= 222635 Pa=> 2.19 atm