Volumetric and Mass Flow Rate (pp. 168-174)¶

Consider a conduit with cross section area, $A$ .

The volume of fluid that passes area $A$ at location $x$ in some time interval $\Delta t$ is given by $A \Delta x = V$

The flow rate is $Q = \frac{V}{\Delta t} = \frac{\Delta x}{\Delta t}A$ , the “velocity term” $u = \frac{\Delta x}{\Delta t}$ is the “mean section velocity”.

If the velocity varies over the cross section one can obtain the mean section velocity by integration; and in fact this is how streamflow is determined.

If the orientation is not orthogonal the integrals are the result of the inner product of the velocity vector $\bar V$ and the area vector $\bar {dA}$

The mass flow rate is the product of the volumetric rate and the fluid density

As with volume, the mass flows also are obtained by inner products as:

Example: Flow in a Rectangular Conduit¶

Example: Flow in a Triangular Conduit¶

Engineering Fluid Mechanics

Volumetric and Mass Flow Rate (pp. 168-174)¶

Example: Flow in a Rectangular Conduit¶

Example: Flow in a Triangular Conduit¶