Calculate the annual electrical power consumption in GWh, due to pumping operation, based on the given data for a centrifugal pump.

Steps to Solve

1. Calculate the Hydraulic Power Required
   Hydraulic power ($P_h$) can be calculated using the formula:
   $$ P_h = \text{Head} \times \text{Discharge rate} \times \text{Specific weight} $$
   Where:

• Head = 180 m
• Discharge rate = 320 m³/hr = $\frac{320}{3600}$ m³/s (conversion to m³/s)
• Specific weight = 10.20 kN/m³

Substituting the values:
$$ P_h = 180 \times \frac{320}{3600} \times 10.20 $$

2. Convert the Hydraulic Power to Electrical Power
   To find the electrical power ($P_e$) consumed, divide the hydraulic power by the overall efficiency ($\eta$):
   $$ P_e = \frac{P_h}{\eta} $$
   Where efficiency $\eta$ = 0.70.

3. Calculate the Total Operating Time in Hours
   The total operating hours in a year consists of two parts:

• For the first 270 days:
  $$ 270 \text{ days} \times 14 \text{ hours/day} = 3780 \text{ hours} $$
• For the remaining 95 days:
  $$ 95 \text{ days} \times 20 \text{ hours/day} = 1900 \text{ hours} $$
  Total operating time:
  $$ \text{Total hours} = 3780 + 1900 $$

4. Calculate the Annual Power Consumption
   The annual power consumption ($E$) in kilowatt-hours (kWh) is given by:
   $$ E = P_e \times \text{Total hours} $$
   To convert it to GWh:
   $$ E_{\text{GWh}} = \frac{E}{1000} $$

5. Perform the Final Calculations

• Compute each step using the above formulas to find the final annual electrical power consumption in GWh.