Question

A pipe contains a gradually tapering section in which its diameter decreases from 400 mm to 250 mm. The pipe contains an incompressible fluid of density 1000 kgm−3 and runs full. If the flow velocity is 2 ms−1 in the smaller diameter, determine the velocity in the larger diameter, the volume flow rate and the mass flow rate.

Answer 1

The velocity in the larger diameter

$v_1S_1=v_2S_2\to v_2=\frac{v_1S_1}{S_2}=\frac{2\cdot3.14\cdot(0.25/2)^2}{3.14\cdot(0.4/2)^2}=0.78 m/s$

The volume flow rate

$Q_V=\frac{V}{t}=\frac{S_2\cdot v_2\cdot t}{t}=3.14\cdot(\frac{0.4}{2})^2\cdot0.78=0.098m^3/s$

The mass flow rate

$Q_m=Q_V\cdot\rho=0.098\cdot1000=98kg/s$