Question

A viscous fluid is flowing through two horizontal pipes. They have the same length, although the radius of one pipe is three times as large as the other. The pressure difference P2 - P1 between the ends of each pipe is the same. If the volume flow rate in the narrower pipe is QA = 2.94 × 102 m3/s, what is the volume flow rate QB in the wider pipe?

Answer 1

The conservation of the mass of fluid through two sections (be they A1 and A2) of a conduit (pipe) or current tube establishes that the mass that enters is equal to the mass that exits. Mathematically the input flow must be the same as the output flow,

$Q_1 = Q_2$

The definition of flow is given by

$Q =VA$

Where

V = Velocity

A = Area

The units of the flow of flow are cubic meters per second, that is to say that if there is a continuity, the volume of input must be the same as that of output, what changes if the sections are modified are the proportions of speed.

In this way

$Q_A = Q_B$

$Q_B = 2.94*10^2 m^3/s$