What is the difference in pressure needed to lift water 15ft in a three inch pipe on the vertical and the pressure needed to push water 15ft in a 3 inch pipe on a 45 degree incline?

To find the difference in pressure required to lift water 15 ft vertically in a three-inch pipe and to push water 15 ft up a 45-degree incline in a three-inch pipe, we need to consider the effects of gravity and inclination.

When lifting water vertically, the only force acting against the flow is gravity. The pressure required to lift the water can be calculated using the formula:

Pressure = density × gravitational acceleration × height

In this case, the height is 15 ft.

On the other hand, when water is pushed up a 45-degree incline, the force required is a combination of the effects of gravity and the inclination. The pressure required can be calculated using the formula:

Pressure = density × gravitational acceleration × height × (1 + sin(incline angle))

For a 45-degree incline, the sin(45) = √2/2 ≈ 0.707. Therefore, the formula becomes:

Pressure = density × gravitational acceleration × height × (1 + 0.707)

To calculate the difference in pressure between these two scenarios, we subtract the pressure required for lifting water (vertical) from the pressure required for pushing water up a 45-degree incline.

In summary,
1. To lift water 15 ft vertically in a three-inch pipe: Pressure = density × gravitational acceleration × 15 ft
2. To push water up a 45-degree incline in a three-inch pipe: Pressure = density × gravitational acceleration × 15 ft × (1 + 0.707)
3. The difference in pressure: Pressure (45-degree incline) - Pressure (vertical)