Determining Maximum Flow Rate and Pressure Difference in a Pump System
Calculating Maximum Flow Rate:
To determine the maximum flow rate of water in the system, we can use Bernoulli's equation and fluid mechanics principles.
According to Bernoulli's equation, the total energy of the fluid flowing in the pipe is conserved. We can use the equation A1v1 = A2v2 to calculate the maximum flow rate, where A1 and A2 are the cross-sectional areas of the pipe at the intake and discharge sides, and v1 and v2 are the velocities of the water at those points.
Given that the pump is 78% efficient and has a power output of 5 kW, we can determine the work done by the pump and subsequently find the maximum flow rate of water being pumped.
Calculating Pressure Difference:
To calculate the pressure difference between the pump inlet and the outlet, we can use the equation P2 - P1 = (1/2)Ï(v2^2 - v1^2).
The pressure difference can be determined by evaluating the velocities of the water at the pump inlet and the outlet, and considering the density of the fluid (water).
By substituting the given values into the equation, we can find the pressure difference between the two points in the system.