What must the water pressure be to supply the second floor (18.0 ft/up) with a pressure of 50.0 lb/in² at that level?

To find the required water pressure to supply the second floor, we can use the concept of pressure in a fluid. The equation for pressure in a liquid is given by:

Pressure = Density × gravitational acceleration × height

In this case, we are given the pressure at the second floor, the height from the ground floor to the second floor, and we need to find the water pressure needed to supply the second floor.

Step 1: Convert the height from feet to inches.
Since the given height is in feet and the pressure is given in pounds per square inch (lb/in²), we need to convert the height from feet to inches since the gravitational constant is in inches.

1 foot = 12 inches

So, 18.0 ft = 18.0 ft × 12 in/ft = 216.0 in

Step 2: Convert the pressure to the proper unit.
To solve for the water pressure, we need the pressure in the same units as the given value of 50.0 lb/in². So, no conversion is required in this step.

Step 3: Calculate the water pressure.
Using the equation for pressure:

Pressure = Density × gravitational acceleration × height

We know that the density of water is approximately 62.4 lb/ft³, and the acceleration due to gravity is approximately 32.2 ft/s².

Plugging in the values:

Pressure = 62.4 lb/ft³ × 32.2 ft/s² × 216.0 in

Step 4: Simplify and calculate the water pressure.
Converting in² to ft² by dividing by 144 (since 1 ft² = 144 in²):

Pressure = (62.4 lb/ft³ × 32.2 ft/s² × 216.0 in) ÷ 144 in²

Simplifying:

Pressure = (62.4 lb/ft³ × 32.2 ft/s² × 216.0 in) ÷ (144 in²)

Pressure ≈ 72.857 lb/ft²

Therefore, the water pressure needed to supply the second floor at a pressure of 50.0 lb/in² is approximately 72.857 lb/ft².