His cold-water supply system serves a bathroom in a multistory building. The architect
directed the piping to be installed in the wall cavities with the main branch above ceiling
level. The supply pipe construction is 4 type-L copper. The building supply is capable of
maintaining a flow rate of 10 gallons per minute. The walls contain a 6-inch cavity, and the
ceilings contain a 12-inch cavity. Consider the installation to be centered in the available
cavity space.
If the cold-water supply pressure to the floor represented in the drawing measures 50 psi
and the flush-valve manufacturer specifies a minimum working pressure of 25 psi, how many
stories can be constructed before friction losses prevent proper valve operation?
A. None including this floor
B. This floor and one more story
C. This floor and two more stories
D. This floor only
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.
Solve for x. -8x+44>_60 and -4x+50<58
-8x + 44 ≥ 60
Subtracting 44 from both sides, we get:
-8x ≥ 16
Dividing both sides by -8 (and reversing the inequality since we are dividing by a negative number), we get:
x ≤ -2
Next:
-4x + 50 < 58
Subtracting 50 from both sides, we get:
-4x < 8
Dividing both sides by -4 (and reversing the inequality), we get:
x > -2
Putting the two inequalities together, we get:
-2 < x ≤ -2
This means that the solution for x is x = -2.
3. What conclusion could the marketing team make about male and female preferences for veggie pizza? Justify your answer.
Without any data or research to draw from, it is impossible to make a reliable conclusion about male and female preferences for veggie pizza. Preferences for food can be influenced by a wide range of factors, including cultural background, personal tastes, dietary restrictions, and individual preferences.
However, if a study were conducted and significant differences were found between male and female preferences for veggie pizza, conclusions could be drawn based on the results of the study. For example, if the study found that a higher proportion of women than men preferred veggie pizza, the marketing team could consider adjusting their marketing strategy to target more women. Alternatively, if the study found that men preferred veggie pizza more than women, the marketing team could consider using this information to develop more effective targeted marketing strategies for male audiences. Ultimately, the conclusions that can be drawn about male and female preferences for veggie pizza (or any other type of food) are dependent on the data and research available.
To determine how many stories can be constructed before friction losses prevent proper valve operation, we need to calculate the pressure drop due to friction along the length of the supply pipe.
First, let's determine the flow rate in gallons per second. Given that the flow rate is 10 gallons per minute, we can convert it to gallons per second:
Flow rate = 10 gallons per minute = 10/60 gallons per second ≈ 0.1667 gallons per second
Now, let's calculate the frictional pressure drop using the Darcy-Weisbach equation:
ΔP = f * (L/D) * (V^2/2g)
Where:
ΔP = pressure drop
f = friction factor
L = pipe length
D = pipe diameter
V = flow velocity
g = acceleration due to gravity
Since the supply pipe construction is 4 type-L copper, we can look up the friction factor for this type of pipe in a hydraulic engineering reference. Let's assume a friction factor of 0.02.
Since the main branch is above ceiling level, we need to calculate the total length of the supply pipe, considering the wall and ceiling cavities. Let's assume each story has a height of 10 feet.
Length of supply pipe = (number of stories) * (height per story) + (wall cavity length) + (ceiling cavity length)
Given that the wall cavity is 6 inches and the ceiling cavity is 12 inches, we convert them to feet:
Wall cavity length = 6 inches = 6/12 feet = 0.5 feet
Ceiling cavity length = 12 inches = 12/12 feet = 1 feet
Now let's consider the flush-valve manufacturer's minimum working pressure requirement of 25 psi. To ensure proper valve operation, the pressure at the floor level should not drop below this value.
Hence, the pressure drop allowed for friction losses is:
Pressure drop allowed = 50 psi - 25 psi = 25 psi
Now we can calculate the number of stories that can be constructed before the pressure drop due to friction losses exceeds the allowed pressure drop.
Let's assume a nominal pipe diameter of 1 inch (0.0833 feet) for a type-L copper pipe:
D = 0.0833 feet
Given the flow rate (V) of 0.1667 gallons per second and knowing that 1 gallon is approximately equal to 0.1337 cubic feet, we can calculate the flow velocity:
V = flow rate / (pipe cross-sectional area)
= 0.1667 gallons per second / (0.1337 cubic feet per gallon * (π*D^2)/4)
≈ 94.12 feet per second
Now we have all the values needed to calculate the pressure drop:
ΔP = 0.02 * (L/D) * (V^2/2g)
Setting ΔP equal to the allowed pressure drop (25 psi), we can solve for L:
25 psi = 0.02 * (L/D) * (V^2/2g)
Simplifying the equation:
L = (25 psi * 2g * D) / (0.02 * V^2)
Substituting the known values:
L = (25 psi * 2 * 32.17 ft/s^2 * 0.0833 ft) / (0.02 * (94.12 ft/s)^2)
L ≈ 2.57 ft
Since each story has a height of 10 feet, the number of stories that can be constructed is the total pipe length (L) divided by the story height:
Number of stories = L / (height per story)
= 2.57 ft / 10 ft
≈ 0.257
Since we cannot construct a fraction of a story, the answer is:
D. This floor only
Friction losses along the supply pipe will exceed the allowed pressure drop after constructing this floor.