Question

Water at a pressure of 7 atm at street level flows into a tall building at 1.5 m/s through a 6 cm diameter pipe. The pipe tapers down to 2 cm on the top floor, 60 m from the ground.

What is the pressure in the faucet on the top floor?

A.

23.2 kPa

B.

28.4 kPa

C.

31.1 kPa

D.

33.6 kPa

Answer 1

Concept required - the question requires the concept of Bernoulli's theorem. Let's see this now..

Solution -

We are given the following data :

P₁ = 7 atm , v₁ = 1.5 m/s ,

d₁= 6cm = 0.06 m , d₂ = 2cm = 0.02 m ,

h= 60m , g =98m/s² , density = 1000 kg/m²

For the water in the pipe -

where S is the surface area , and v is the velocity

So putting the values, we find that :

Thus the flow velocity on the top floor will be:

Applying Bernoulli's theorem on the ground floor and top floor, we get:

where

p= water density , g =acceleration due to gravity , h₁= elevation of pipe at ground level

h₂ = elevation of pipe on top floor , P₁ = pressure at street level , P₂ = Pressure on the faucet at top floor

Also we know that , h₁= 0 , h₂= h = 60m

Converting the gauge pressure to Pa -

Putting the values, we get :

Due to the value of g, there might be slight approximation in our answer. Hence the correct answer is Option B