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Finite Volume Analysis: Application of Conservation of Linear Momentum

Example 1 A variable mesh screen produces a linear and axisymmetric velocity profile

in the air flow through a 2 ft diameter circular cross-section duct as shown below. The

static pressures upstream and downstream of the screen are 0.2 psi and 0.15 psi and are

uniformly distributed over the flow cross sectional area. Neglect friction exerted by the

duct wall on the flowing air. Find the screen drag force.

Strategy for solution: Note we have a two-part solution. First find the velocity profile for

section 2. Then use it to find the drag force by the screen.

Step 1	Identify (draw) the control surface and control volume for the fluid flow. Show the unit outward normal to surfaces across which flow occurs.
Step 2	Write the equation for conservation of mass and simplify for known values. Check for steady flow. Use to find the velocity profile at section 2.
Step 3	Write the equation for conservation of linear momentum and simplify for known values. Check for steady flow. Include pressure forces and the drag force by the screen.
Step 4	Solve for desired value, the drag force.