**Problem Analysis:**
To estimate the power required for the pump, we need to consider the following factors:
1. Flow rate of the oil
2. Specific gravity of the oil
3. Viscosity of the oil
4. Diameter and length of the pipeline
5. Elevation difference between the inlet and outlet of the pipeline
6. Efficiency of the pump

**Solution:**

1. **Flow Rate of the Oil:**

Given: Flow rate = 420 litres/min

To convert the flow rate to cubic meters per second (m^3/s), we can use the following conversion:

1 litre = 0.001 cubic meters
1 minute = 1/60 seconds

Therefore, flow rate = (420 * 0.001) / (60) = 0.007 m^3/s

2. **Specific Gravity of the Oil:**

Given: Specific gravity = 0.91

Specific gravity is the ratio of the density of a substance to the density of a reference substance (usually water).

Since the specific gravity is less than 1, the oil is lighter than water.

3. **Viscosity of the Oil:**

Given: Viscosity = 1.24 poise

Viscosity is a measure of a fluid's resistance to flow. It determines how easily a fluid can flow through a pipe.

4. **Diameter and Length of the Pipeline:**

Given: Diameter = 75 mm

To calculate the cross-sectional area of the pipeline, we can use the formula for the area of a circle:

Area = π * (diameter/2)^2

Area = π * (75/2)^2 = 4427.92 mm^2

To convert the area to square meters (m^2), we divide by 1,000,000:

Area = 4427.92 / 1,000,000 = 0.00442792 m^2

Given: Length = 62 m

5. **Elevation Difference:**

Given: Outlet elevation - Inlet elevation = 3 m

6. **Efficiency of the Pump:**

Given: Efficiency = 60%

Efficiency is the ratio of the useful power output of a machine to the power input.

To estimate the power required for the pump, we can use the following formula:

Power = (Flow rate * Specific gravity * Viscosity * Head) / (Efficiency * Pumping power factor)

Where:
- Flow rate is the volume of fluid flowing per unit time (m^3/s).
- Specific gravity is the ratio of the density of the fluid to the density of a reference fluid (dimensionless).
- Viscosity is a measure of a fluid's resistance to flow (poise).
- Head is the difference in elevation between the inlet and outlet of the pipeline (m).
- Efficiency is the ratio of the useful power output to the power input (dimensionless).
- Pumping power factor accounts for the effect of pipe friction and other losses (dimensionless).

Let's calculate the power required for the pump using the given values:

Power = (0.007 * 0.91 * 1.24 * 3) / (0.60 * Pumping power factor)

The pumping power factor depends on the flow rate, pipe diameter, and other factors. It can be determined using empirical correlations or experimental data.

Since the pumping power factor is not given