Final answer:
The volume flow rate in the pipe can be calculated using the principle of Bernoulli's equation. Assuming steady flow and neglecting viscosity, the sum of the pressure, kinetic energy per unit volume, and potential energy per unit volume should be constant along the pipe.
Step-by-step explanation:
The volume flow rate in the pipe can be calculated using the principle of Bernoulli's equation. Assuming steady flow and neglecting viscosity, the sum of the pressure, kinetic energy per unit volume, and potential energy per unit volume should be constant along the pipe.
Since the nozzle discharges to the atmosphere, the pressure at the outlet of the pipe can be considered atmospheric pressure, which is typically 1 atmosphere or 101,325 Pa. The pressure difference between the inlet and outlet of the pipe is needed to keep the nozzle attached to the pipe.
To calculate the volume flow rate, we can use the equation:
Q = (pi/4) * D^2 * √(2 * (P_in - P_out) / ρ)
Where:
- Q is the volume flow rate
- D is the diameter of the pipe
- P_in is the pressure at the inlet of the pipe
- P_out is the pressure at the outlet of the pipe
- ρ is the density of the fluid
Given that the outlet diameter of the nozzle is 20mm (or 0.020m) and the inlet diameter of the pipe is 50mm (or 0.050m), we can substitute these values into the equation along with the known pressure difference of 45.5N and solve for the volume flow rate.
Q = (pi/4) * (0.050^2) * √(2 * (45.5) / 1000)
Q ≈ 0.012 m^3/s