What is the absolute pressure required by the water pump to reach the 13th floor?

Question

A water pump is located on the first floor of a 13 floor building. The water pump releases water at a pressure of 35lb/in^2. If the distance between each floor is 10ft, what is the absolute pressure required by the water pump to reach the 13th floor?

Answer 1

Hey Derek, here are the steps for this calculation:

1. Determine the height difference: Calculate the total height the water needs to be pumped. Each floor is 10 feet high, and there are 13 floors. Therefore, the total height is: 10 ft/floor × 13 floors=130 ft
2. Convert height to pressure: Use the relationship between height and pressure in a fluid. The pressure increase due to a height difference hhh in feet can be calculated using the equation: P=ρgh. where ρ is the density of water (62.4 lb/ft³), g is the acceleration due to gravity (32.2 ft/s²), and h is the height in feet. The pressure in lb/ft² can be converted to lb/in² by dividing by 144 (since there are 144 in² in 1 ft²).
3. Calculate pressure increase: The pressure increase ΔP in lb/ft² is: ΔP = 62.4 lb/ft3 × 32.2 ft/s2 × 130 ft = 261,504 lb/ft2 (≈ 1,815.33 lb/in²)
4. Total required pressure: The water pump initially releases water at 35 lb/in². Add the pressure increase to the initial pump pressure to find the absolute pressure required at the pump: Ptotal=35 lb/in² + 1,815.33 lb/in² = 1850.33 lb/in²

Thus, the absolute pressure required by the water pump to ensure water reaches the 13th floor is approximately 1850.33 lb/in².

Best,

Andrew