Answer: D
Explanation:
To determine the maximum number of stories that can be constructed before friction losses prevent proper valve operation, we need to calculate the pressure loss due to friction as the water flows through the piping to each floor.
Using the Hazen-Williams formula, which is commonly used for sizing water supply systems:
P = (4.52Q1.85L10.67/C1.85)d4.87
where:
P = pressure loss due to friction (psi)
Q = flow rate (gpm)
L = length of pipe (feet)
C = Hazen-Williams coefficient (dimensionless)
d = inside diameter of pipe (inches)
Assuming the flow rate is 10 gpm, the length of pipe from floor to floor is the height of the building divided by the number of stories, and the inside diameter of the pipe is 4 inches (since 4 type-L copper corresponds to a 4-inch nominal diameter), the pressure loss for each story can be calculated using a Hazen-Williams coefficient of 130 for copper piping:
P = (4.52 x 10^1.85 x (1 story height/number of stories)10.67/1301.85)4.87
P = 3.3 x (1/number of stories)^1.85
For example, for a 2-story building, the pressure loss would be:
P = 3.3 x (1/2)^1.85
P = 1.6 psi
To ensure that the minimum working pressure of 25 psi is maintained at each flush valve, the pressure loss for each story cannot exceed 25 - 50 = -25 psi (since lower pressures can cause valve malfunctions).
Solving for the maximum number of stories:
3.3 x (1/number of stories)^1.85 <= -25
(1/number of stories)^1.85 <= -25/3.3
1/number of stories <= (-25/3.3)^0.54
number of stories >= 1/(-25/3.3)^0.54
number of stories >= 6.7
Therefore, the maximum number of stories that can be constructed before friction losses prevent proper valve operation is D. This floor only.