To begin with, we need to understand that pressure and flow rate are directly proportional. This means that the greater the pressure, the higher the flow rate. Since the pressure changes from 14 KPa to 4 KPa, the flow rate will decrease. To calculate the actual flow rate, we need to use the formula:
Q = A1V1 = A2V2
Where Q is flow rate, A is the cross-sectional area of the pipe, and V is the velocity of the fluid. In this case, A1 = (π/4) x 0.6^2 = 0.2827 m^2, A2 = (π/4) x 0.9^2 = 0.635 m^2, and V1 is given as V2 = Q/A2. Thus, we can calculate V1 as 16.11 m/s, and V2 as 7.87 m/s. Now, we can calculate the actual flow rate as:
Q = A1V1 = 0.2827 x 16.11 = 4.55 m^3/s
Since we were given the flow rate as 500 liters per second, we can convert this to cubic meters per second by dividing by 1000. Thus:
Q = 0.5 / 1000 = 0.0005 m^3/s
We can now calculate the power supplied to the motor by using the formula:
P = ρQgΔh
Where P is power, ρ is the density of water, Q is flow rate, g is gravitational acceleration, and Δh is the difference in height between the intake and exhaust pipes. In this case, ρ = 1000 kg/m^3, g = 9.81 m/s^2, and Δh = 2.5 m. Substituting these values, we get:
P = 1000 x 0.0005 x 9.81 x 2.5 = 12.26 watts
Thus, the power supplied to the motor is 12.26 watts.
In conclusion, we can see that the diameter of the pipe has a significant impact on the flow rate, which in turn affects the power supplied to the motor. Graphite electrodes are widely used in the manufacture of such pipes, as they exhibit excellent thermal and chemical resistance. By optimizing the design of the pipe, we can ensure efficient flow of water to the motor and enhance its performance.