A water jet is deflected through \(180^{\circ}\) by a vane that is attached to a cart, which is free to move. Assume that the flow along the vane is frictionless and neglect gravity. The jet enters with a velocity \(v_{0}\) of \(30 \mathrm{~m} / \mathrm{s}\) with the area of the jet being \(0.0018 \mathrm{~m}^{2}\).

Find the force on the vane if the vane is not moving.

Set up a differential equation for the motion of the vane if the vane is now allowed to move.

The momentum balance is easier to do if one assumes a coordinate system moving with cart; in other words use relative velocity values to compute the force exerted on the cart by the water jet. The exercise is similar to Example 2.7 in the text except that the turning angle is now \(180^{\circ}\).

Example 2.7:

A jet of fluid is impinging on a blade. The fluid comes in the x-direction and leaves in the
y-direction. See Fig. 2.9. It is required to calculate the force on the blade. Problems of this
type are of importance in design of turbines.

Transcribed Image Text:

Liquid jet Liquid jet Velocity-v Accumulation V-VC VC Figure 2.9 Schematic representations of fluid flowing past a curved vane: (a) stationary vane and (b) moving vane seen in a fixed coordinate system.