Calculating Reduced Velocity When Pipe Enlarges
What is the scenario presented in the data?
The data provides information about the flow of water in a pipe with a diameter of 2.5 inches at a velocity of 61 ft/sec, and then the pipe enlarges to a diameter of 5 inches.
What needs to be calculated based on the scenario?
The reduced velocity of the water flow needs to be calculated when the pipe enlarges from 2.5 inches to 5 inches in diameter.
Answer:
The reduced velocity can be calculated using the principle of continuity. The reduced velocity is approximately 5.06 ft/sec.
Explanation:
To calculate the reduced velocity, we can use the principle of continuity, which states that the mass flow rate is constant in a closed system. The equation for continuity is given by:
A₁ * v₁ = A₂ * v₂
Where A₁ and A₂ are the cross-sectional areas of the pipe before and after the enlargement, and v₁ and v₂ are the velocities of the water before and after the enlargement.
In this case, the initial diameter of the pipe is 2.5 inches, which corresponds to a radius of 0.03175 meters. The final diameter is 5 inches, which corresponds to a radius of 0.0635 meters.
Using the equation A₁ * v₁ = A₂ * v₂, we can find that the reduced velocity is approximately 5.06 ft/sec.