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Finite Volume Analysis: Application of Conservation of Mass

Example 1 A viscous liquid flows over a flat plate of width, L, into the paper as shown

in the figure below. The layer of fluid near the plate is called the boundary layer. At

the leading edge of the plate, the velocity profile is approximately uniform with a value

of U. At a distance, x, down the plate the velocity profile in the boundary layer is

given as follows:

u/U = ( y/δ)^1/7

Find an expression for the volumetric flowrate, Q , in terms of U, L, and δ from the

leading edge to a location downstream at a distance, x, where the boundary layer

thickness is δ.

Strategy for solution:

Step 1

Identify (draw) the control surface and control volume for the fluid flow.

Step 2

Write the equation for conservation of mass and simplify for known

values. Check for steady flow. Identify surfaces across which flow occurs.

Step 3

Solve for desired values.