Calculating Pipe Discharge for Power Transmission
Understanding the Problem
A pipe with a diameter of 0.6 m and a length of 3 km connects two reservoirs, transmitting 71 kW of power optimally at the outlet. The pipe wall has a fanning friction coefficient of 0.006. We are tasked with determining the pipe discharge or volumetric flow rate. The water density is given as 1000 kg/m².
Solving for Pipe Discharge
Flow rate: The pipe discharge is found to be 0.36 m/s by utilizing power and head calculations involving friction, length, discharge, and diameter.
To find the discharge or volumetric flow rate, we apply the formula for power transmission through liquids: P = ηQHρ, where P is the power, η is the efficiency, Q is the discharge, H is the head, and ρ is the density.
The head (H) can be determined using the formula: H = 4fLQ²/d⁵, where f is the fanning friction coefficient, L is the length, Q is the discharge, and d is the diameter of the pipe. By substituting the provided values into the equation and rearranging, we arrive at an answer of 0.36 m/s for the pipe discharge.
How is the pipe discharge calculated for power transmission in this scenario? The pipe discharge is calculated by applying power and head calculations involving friction, length, discharge, and diameter. The formula P = ηQHρ is used, where P is the power, η is the efficiency, Q is the discharge, H is the head, and ρ is the density. Additionally, the head (H) is determined using the formula H = 4fLQ²/d⁵, where f is the fanning friction coefficient, L is the length, Q is the discharge, and d is the diameter of the pipe. Substituting the values and rearranging the equations yields a pipe discharge of 0.36 m/s.