This document contains examples of calculating forces on objects from impinging water jets or flowing through pipes and bends. The examples calculate the forces on plates from impinging water jets moving at various velocities relative to the plate. Other examples calculate the forces on stationary or moving vanes used to deflect water jets. Further examples determine the forces on bends and reducers in pipelines due to water flowing through them.

1. HYDRODYNAMICS

9. Example 1. A jet of water 25mm in diameter and having a velocity of
7.5 m/s strikes against a plate at right angles. Determine the force on
the plate
a. If the plate is stationary
b. If the plate is moving in the same direction as the jet at a speed of 3m/s
c. If the plate is moving towards the nozzle with a velocity 4 m/s

11. Example 2. A 50mm diameter horizontal jet of water strikes a flat plate
as shown. Determine the jet velocity if an 80N horizontal force is
required to permit the plate
a. To move at a constant speed of 2m/s to the right
b. Stationary
c. To move at a constant speed of 2m/s to the left

13. Example 3. A horizontal jet of water flowing freely in the atmosphere is
deflected through an angle of 90° by a fixed curve vane. If the water jet
has a diameter of 40mm and a velocity of 8m/s, what is the force
required to hold the vane in place?

15. Example 4. A jet having a diameter of 50mm and a velocity of 15m/s is
deflected by a vane which is curved through an angle 60°.Determine X
and Y components of the force exerted by the jet and its direction as it
leaves the vane.
a. If the vane is stationary
b. If the vane is moving with a velocity of 6m/s in the same direction
as the jet.

17. Example 5. The water jet shown in the figure is moving at 13.72 m/s, is
split so that one third of the water moves toward A. Assuming ideal
flow in a horizontal plane. Compute the horizontal and vertical
component of the force on the stationary splitter.

19. FORCES DEVELOPED ON CLOSED CONDUITS

21. Example 1. A 45°, 300mm x 200mm reducing bend in a level pipeline
carries water at a rate of 300 lit/s. Determine the components of the
force necessary to hold the bend in position. The pressure at the
entrance is 345 kPa and the friction in the bend is negligible.

23. Example 2. Water under a pressure of 350 kPa, flows with a velocity of 3m/s
through a right-angle bend having a uniform diameter of 300mm. The bend
lies in a horizontal plane; water enters from west and leaves towards the
north. Assuming no drop in pressure, what is the magnitude and direction of
the resultant force acting on the bend?