Question

A 7.0-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 32.0 kPa and 25.0 kPa , respectively.

What is the volume rate of flow?

Express your answer using two significant figures.

Answer 1

Here,

radius of the 7 cm pipe, r1 = 7/2 = 3.5 cm

radius of pipe, r2 = 5/2 = 2.5 cm

let the speed of the flow is v1 and v2

Using equation of continuity

pi * 3.5^2 * v1 = pi * 2.5^2 * v2

Using Bernoulli's equation

P1 + 0.50 * p * v1^2 = P2 + 0.50 * p * v2^2

32000 + 0.50 * 1000 * v1^2 = 25000 + 0.50 * 1000 * v2^2

solving for v1 and v2

v1 = 2.22 m/s

v2 = 4.35 m/s

volume flow rate = pi * r1^2 * v1

volume flow rate = pi * 0.035^2 * 2.22

volume flow rate = 0.0085 m^3/s

the volume flow rate is 0.0085 m³/s