Jet of water striking series of radial flat vanes of the wheel is 200 mm and the velocity of the jet is 100 m/s. The velocity of the vanes is 46 m/s
Calculate the force exerted on the series of vanes by the jet of water.
To calculate the force exerted on the series of vanes by the jet of water, we can use the principle of momentum change.
The force exerted by the jet of water on the vanes is equal to the rate of change of momentum. The momentum of the jet of water can be calculated by multiplying its mass by its velocity.
The given information includes the jet diameter and velocity, but we need to calculate the mass of the water jet first.
The formula to calculate the mass flow rate is given by:
mass flow rate = density of water * area of the jet * velocity of the jet
First, we need to calculate the area of the jet. The area of a circular section is given by the formula:
Area = π * (diameter/2)^2
Given that the diameter of the jet is 200 mm, we can substitute this value into the equation:
Area = π * (0.2 m / 2)^2 = 0.0314 m^2.
Next, we can calculate the mass flow rate:
mass flow rate = density of water * area of the jet * velocity of the jet
mass flow rate = 1000 kg/m^3 * 0.0314 m^2 * 100 m/s
mass flow rate = 314 kg/s
Now, we can calculate the force exerted on the vanes. The force is equal to the rate of change of momentum, which is given by:
Force = mass flow rate * (velocity of the vanes - velocity of the jet)
Given that the velocity of the vanes is 46 m/s, we can substitute the values into the equation:
Force = 314 kg/s * (46 m/s - 100 m/s)
Force = 314 kg/s * (-54 m/s)
Force = -16956 N
The result is -16956 N, which means the force exerted on the vanes by the jet of water is 16956 N in the opposite direction of the jet.