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Finite Volume Analysis: Application of Conservation of Linear Momentum

Example 3 A horizontal circular jet of air strikes a stationary plate as shown in the

figure below. The speed of the jet is 30 m/sec and its diameter is 40 mm. Assume the

plate is frictionless and that the magnitude of the speed of the jet remains constant as the

air passes over the fixed plate. Find the resultant normal force, R, to anchor the plate.

Also find the fraction of mass rate at both exits along the plate.

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. The

figure above shows a top view of the plate with the control surface, control volume, and the unit outward normals n₁, n₂, and n₃. Let n be the unit normal to the plate. i.e. n = ˗ sin θ i + cos θ j .

Step 2

Write the equations for conservation of mass and of linear momentum.

Determine the normal component of linear momentum and the component

of linear momentum along the plate using the dot product.

Step 3

Solve for desired anchoring force. Solve for the mass rates at each of the

exits along the plate.

Click here to continue with this example.

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