Question (1) 7 Marks A jet of water 50 mm in diameter moving at 18 m/s strikes a plate inclined anti-clockwise 115º from the horizontal (25º from the vertical). Determine: A. Force on the plate when, The force on the plate when the jet of water strikes at an angle of 115º from the horizontal and 25º from the vertical is to be determined. What is the formula to calculate the force exerted by the jet of water on the plate?
The force exerted by the jet of water on the plate can be calculated using the formula:
F = 1/2 × ρ × A × V^2 × C
Where:
- F = Force exerted by the jet of water (in Newtons),
- ρ = Density of water (in kg/m³),
- A = Area of the jet (in m²),
- V = Velocity of the jet (in m/s),
- C = Coefficient of the jet (dimensionless).
Given that the diameter of the jet (d) is 50 mm, the area (A) can be calculated as (A = π x d^2 / 4).
The angle of inclination (θ) from the horizontal is 115º, which means the angle of the jet with respect to the vertical (β) is 90º - θ = 90º - 115º = -25º. We need to take the absolute value, so β = 25º.
The coefficient C depends on β. For β = 25º, the coefficient is approximately 1.0.
Next, the density of water is ρ = 1000 kg/m³ and the velocity (V) is 18 m/s.
Now, we can plug the values into the formula:
F = 1/2 × 1000 × 4π × (0.05)^2 × 18^2 × 1.0
After calculating the above expression, we get the force exerted by the jet of water on the plate.
Calculation Details:
The force exerted by a jet of water on a plate is determined by various factors such as the density of water, the area of the jet, the velocity of the jet, and the coefficient of the jet. In this scenario, we are given specific values for each of these parameters which allow us to calculate the force exerted by the water jet on the inclined plate.
Density of Water (ρ):
The density of water is a crucial factor in determining the force exerted by the jet. In this case, the density of water is given as 1000 kg/m³, which is a standard value for water.
Area of the Jet (A):
The area of the jet is calculated using the diameter of the jet. The diameter provided is 50 mm, which needs to be converted to meters for consistency with other units in the formula. By using the formula for the area of a circle (A = π x d^2 / 4), we can determine the area of the jet.
Velocity of the Jet (V):
The velocity of the jet is specified as 18 m/s. This parameter influences the force exerted by the jet and is a key component in the formula.
Coefficient of the Jet (C):
The coefficient of the jet is dependent on the angle of the jet with respect to the vertical. In this case, the angle is given as 25º, which leads to a coefficient of approximately 1.0. This coefficient accounts for the direction and efficiency of the jet in transferring force to the plate.
After substituting the given values into the formula and performing the calculations, we can determine the force exerted by the jet of water on the inclined plate. This calculation provides valuable insight into the impact and magnitude of the force generated by the water jet, offering a quantitative understanding of the physics involved in such scenarios.
By understanding the formula and the variables involved, we can effectively analyze and predict the force exerted by water jets in various engineering and fluid mechanics applications.