Question

Water is pumped with a 120 kPa compressor entering the lower pipe (1) and flows upward at a speed of 1 m/s. Acceleration due to gravity is 10 m/s and water density is1000 kg/m-3. What is the water pressure on the upper pipe (II).

Answer 1

The water pressure on the upper pipe is 92.5 kPa.

Step-by-step explanation:

Given that,

Pressure in lower pipe= 120 kPa

Speed of water in lower pipe= 1 m/s

Acceleration due to gravity = 10 m/s²

Density of water = 1000 kg/m³

Radius of lower pipe = 12 m

Radius of uppes pipe = 6 m

Height of upper pipe = 2 m

We need to calculate the velocity in upper pipe

Using continuity equation

`A_(1)v_(1)=A_(2)v_(1)`

`\pi r_(1)^2* v_(1)=\pi r_(2)^2* v_(2)`

`v_(2)=(r_(1)^2* v_(1))/(r_(2)^2)`

Put the value into the formula

`v_(2)=(12^2*1)/(6^2)`

`v_(2)=4\ m/s`

We need to calculate the water pressure on the upper pipe

Using bernoulli equation

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

Put the value into the formula

`120*10^(3)+(1)/(2)*1000*1^2+1000*10*0=P_(2)+(1)/(2)*1000*(4)^2+1000*10*2`

`120500=P_(2)+28000`

`P_(2)=120500-28000`

`P_(2)=92500\ Pa`

`P_(2)=92.5\ kPa`

Hence, The water pressure on the upper pipe is 92.5 kPa.