Answer:
To calculate the velocity of the water in the inlet and outlet pipes, we can use the principle of continuity, which states that the volume flow rate is constant throughout the pipe system.
A. Velocity of water in the inlet and outlet pipes:
1. Calculate the cross-sectional area of the pipes:
- Inlet pipe area (A1) = π * (diameter/2)^2
- Outlet pipe area (A2) = π * (diameter/2)^2
2. Calculate the velocity of water in the pipes using the formula:
- Velocity = Volume flow rate / Area
- Volume flow rate = Volume of water entering the tank every two minutes / 120 seconds
B. Pressure at the outlet:
1. Calculate the velocity of water at the outlet pipe using the principle of continuity.
2. Apply the Bernoulli's equation between the surface of the water in the tank and the outlet pipe:
- P1 + 1/2 * ρ * v1^2 + ρ * g * h1 = P2 + 1/2 * ρ * v2^2 + ρ * g * h2
- P1 = Pressure at the surface of the water in the tank (1 atm)
- P2 = Pressure at the outlet
- ρ = Density of water
- v1 = Velocity of water in the inlet pipe
- v2 = Velocity of water in the outlet pipe
- g = Acceleration due to gravity
- h1 = Height of the inlet pipe
- h2 = Height of the outlet pipe
By solving these equations, you can find the velocity of water in the inlet and outlet pipes and calculate the pressure at the outlet.