Problem Statement
Find the force exerted by a jet of water of diameter 100 mm on a stationary flat plate, when the jet strikes the plate normally with a velocity of 30 m/s.
Given Data & Constants
- Diameter of jet, \(d = 100 \, \text{mm} = 0.1 \, \text{m}\)
- Velocity of jet, \(V = 30 \, \text{m/s}\)
- Density of water, \(\rho = 1000 \, \text{kg/m}^3\)
Solution
1. Calculate the Area of the Jet (A)
2. Calculate the Force Exerted by the Jet (F)
The force exerted by the jet on a stationary plate normal to it is equal to the rate of change of momentum of the jet.
The force exerted by the jet on the plate is approximately \(7068.6 \, \text{N}\) or \(7.07 \, \text{kN}\).
Explanation of the Impulse-Momentum Principle
The force calculated is a direct application of Newton's Second Law, expressed in terms of momentum. The law states that the force on an object is equal to the rate of change of its momentum (\(F = \Delta p / \Delta t\)).
In this case, the "object" is the continuous stream of water. As the jet hits the stationary plate, its forward momentum is completely destroyed (its final velocity in the original direction becomes zero). The force on the plate is the reaction to the force required to cause this change in momentum for the water. Since the water flows continuously, this results in a constant, steady force on the plate.
