what is the volume rate of flow?

Question

A 6.8 cm diameter horizontal pipe gradually narrows to 5.2 cm . When water flows through this pipe at a certain rate, the gauge pressure in these two sections is 33.0 kPa and 22.0 kPa , respectively.

Answer 1

Use the bernoulli equation to setup the problem and then use the fact that A₁V₁ = A₂V₂

Where A₁ = cross-section area of the large pipe section & V₁ = the velocity in the large pipe section

D₁ = pipe diameter of the large pipe section

I used english units and got V₁ = 11.1 ft/sec

Then to obtain the volumetric flow, Q = AV = .434 ft³/sec = .0123 m³/sec

(Bernoulli equation) p₁/SW + z₁ + V₁²/2g = p₂/SW + z₂ + V₂²/2g

Where p = pressure, SW = specific weight, z = elevation which is the same for both & thus cancels

g = gravitational constant = 32.2 ft/sec² or 9.8 m/sec²,

and Since A₁V₁ = A₂V₂ then V₂ = (D₁²/D₂²)V₁