Through a pipe of diameter 15.5 cm , water is pumped from the Colorado River up to Grand

Canyon Village, on the rim of the canyon. The
river is at 564 m elevation and the village is at 2096 m .
At what minimum pressure must the water
be pumped to arrive at the village? The
acceleration of gravity is 9.8 m/s
3
.
Answer in units of MPa

I got 15013600 but it's incorrect. Please help me!! Thank you!

To find the minimum pressure required to pump water from the Colorado River up to Grand Canyon Village, we need to consider the change in elevation and the diameter of the pipe.

1. First, let's calculate the difference in elevation between the river and the village: 2096 m - 564 m = 1532 m. This is the vertical distance that the water needs to be pumped.

2. Now, let's convert this elevation difference to pressure. The pressure at any point in a fluid is given by the formula P = ρgh, where P is the pressure, ρ is the density of the fluid, g is the acceleration due to gravity, and h is the height or elevation difference.

3. The density of water, ρ, is approximately 1000 kg/m³.

4. The acceleration due to gravity, g, is given as 9.8 m/s².

5. Plugging in these values into the pressure formula: P = (1000 kg/m³) * (9.8 m/s²) * (1532 m). This will give us the pressure in Pascal (Pa).

6. Finally, to convert Pascal to MegaPascal (MPa), we divide by 1,000,000: P / 1,000,000. This will give us the answer in units of MPa.

Let's perform the calculation:

P = (1000 kg/m³) * (9.8 m/s²) * (1532 m) = 15077440 Pa

Converting to MPa: 15077440 Pa / 1,000,000 = 15.07744 MPa

Therefore, the minimum pressure required to pump the water from the river to the village is approximately 15.07744 MPa.