Question

A 8.0-cm-diameter horizontal pipe gradually narrows to 5.0 cm . When water flows through this pipe at a certain rate, the gauge pressure in these two sections is 31.0 kPa and 25.0 kPa , respectively. What is the volume rate of flow?

Answer 1

Given is:-

Initial diameter = 8cm

Final diameter = 5cm

Initital Pressure P₁ = 31KPa

Final Pressure P₂ = 25KPa

Initial Area of the pipe is  

Final area of the pipe is  

We know that the flow rates must be the same as water is incompressible

or

By putting all the details in above equation, we get

Now by the Bernoulli's theroem

we haven't written potential energy terms because pipe is at same height, thus P.E will remain same.

By putting all the terms in above equation we get

Thus will be

Thus the volume rate of flow will be area multiplied by veloctiy

Initial   or  

similarly the final flow rate will be

(Because flow rate will be remain same)