Answer:
a) The mass flow rate of water is 14.683 kilograms per second.
b) The pressure difference across the pump is 245.175 kilopascals.
Explanation:
a) Let suppose that pump works at steady state. The mass flow rate of the water ([tex]\dot m[/tex]), in kilograms per second, is determined by following formula:
[tex]\dot m = \frac{\eta \cdot \dot W}{g\cdot H}[/tex] (1)
Where:
[tex]\dot W[/tex] - Pump power, in watts.
[tex]\eta[/tex] - Efficiency, no unit.
[tex]g[/tex] - Gravitational acceleration, in meters per square second.
[tex]H[/tex] - Hydrostatic column, in meters.
If we know that [tex]\eta = 0.72[/tex], [tex]\dot W = 5000\,W[/tex], [tex]g = 9.807\,\frac{m}{s^{2}}[/tex] and [tex]H = 25\,m[/tex], then the mass flow rate of water is:
[tex]\dot m = 14.683\,\frac{kg}{s}[/tex]
The mass flow rate of water is 14.683 kilograms per second.
b) The pressure difference across the pump ([tex]\Delta P[/tex]), in pascals, is determined by this equation:
[tex]\Delta P = \rho\cdot g\cdot H[/tex] (2)
Where [tex]\rho[/tex] is the density of water, in kilograms per cubic meter.
If we know that [tex]\rho = 1000\,\frac{kg}{m^{3}}[/tex], [tex]g = 9.807\,\frac{m}{s^{2}}[/tex] and [tex]H = 25\,m[/tex], then the pressure difference is:
[tex]\Delta P = 245175\,Pa[/tex]
The pressure difference across the pump is 245.175 kilopascals.
