To supply the plumbing system of a New York office building, water needs to be pumped to a tank on the roof, where its height will provide a "head" of pressure for all the floors. The vertical height between the basement pump and the level of the water in the tank is 95.3 m. What gauge pressure does the pump have to apply to the water to get it up to the tank?
Should my answer be: P=pgh= (1000kg/m3)(9.80m/s2)(95.3)= 9.34e5 ?
If not, can someone show me what I did wrong. I used 1000 as my density of water, and 9.80 as gravity
You did it correctly. The dimension of the final pressure number is Pascals
Your calculation is correct. The gauge pressure can be calculated using the equation P = pgh, where P is the gauge pressure, p is the density of the fluid (in this case, water), g is the acceleration due to gravity, and h is the vertical height or "head" of the fluid column. In this case, the density of water is indeed 1000 kg/m^3, the acceleration due to gravity is 9.8 m/s^2, and the vertical height is 95.3 m.
So, using the formula:
P = (1000 kg/m^3)(9.8 m/s^2)(95.3 m) = 9.34 x 10^5 Pa
Therefore, the pump needs to apply a gauge pressure of 9.34 x 10^5 Pa to the water to get it up to the tank.
Your formula for calculating the gauge pressure is correct. However, gravity is not exactly 9.80 m/s^2. The actual value of gravity varies depending on the location on Earth. In this case, since you are dealing with a building in New York, you should use the local value of gravity for New York.
To get the correct value of gravity, you can consult a gravity map or use an average value for New York. The average value of gravity in New York City is approximately 9.80665 m/s^2, which is similar to the standard gravity value you used.
Here's the calculation with the correct value of gravity:
P = pgh = (1000 kg/m^3)(9.80665 m/s^2)(95.3 m) = 9.51 x 10^5 Pa
Therefore, the gauge pressure the pump needs to apply to the water is approximately 9.51 x 10^5 Pa.