Question

Water flows through a horiztonal pipe at a rate of 94 ft3/min. A pressure gauge placed on a 3.3 inch diameter section of the pipe reads 15 psi.

What is the gauge pressure in a section of pipe where the diameter is 5.2 inches?

Answer 1

The gauge pressure is 1511.11 psi.

Step-by-step explanation:

Given that,

Flow rate = 94 ft³/min

Diameter d₁=3.3 inch

Diameter d₂ = 5.2 inch

Pressure P₁= 15 psi

We need to calculate the pressure on other side

Using Bernoulli equation

`P_(1)+(1)/(2)\rho v_(1)^2=P_(2)+(1)/(2)\rho v_(2)^2`

We know that,

`V=Av`

`v=(V)/(A)`

Where, V = volume

v = velocity

A = area

Put the value of v into the formula

`P_(1)+(1)/(2)\rho ((V)/(A_(1)))^2=P_(2)+(1)/(2)\rho ((V)/(A_(2)))^2`

Put the value into the formula

`15+(1)/(2)*0.36*((2707.2*4)/(\pi*(3.3)^2))^2=P_(2)+(1)/(2)*0.36*((2707.2*4)/(\pi*(5.2)^2))^2`

`P_(2)=15+(1)/(2)*0.036*((2707.2*4)/(\pi*(3.3)^2))^2-(1)/(2)*0.036*((2707.2*4)/(\pi*(5.2)^2))^2`

`P_(2)=1525.8\ psi`

We need to calculate the gauge pressure

Using formula of gauge pressure

`P_(g)=P_(ab)-P_(atm)`

Put the value into the formula

`P_(g)=1525.8-14.69`

`P_(g)=1511.11\ psi`

Hence, The gauge pressure is 1511.11 psi.