How Can You Calculate the Maximum Flow Rate for a Hot Shower?

In summary: And, since the problem specified working in US Customary units, I think gpm would be appropriate.In summary, the problem is to determine the maximum flow rate of a shower in cubic feet per minute, given a specific set of conditions. After using various equations and constants, the result is that the flow rate should be reported in gallons per minute.
  • #1
frequentPeriod
2
0

Homework Statement


My youngest son likes a hot shower, and wants to stay in the shower as long as possible. We do not have an on-demand water heater. He is a small boy, so he doesn't need that much water. The incoming water supply is at 45 deg F and our water heater is rated at 45,000 BTU/hour. Compute the maximum flow rate of the shower (in cubic feet per minute) so that my son can stay in the shower all day in 95 deg F water.

Initial temperature: 45F
Final Temperature: 95F
Work: 45 000 BTU/hour
Density of water:
Time: 24 hours
Heat Capacity of water = 1
densityWater = 62.428;

Homework Equations


energy = work*time
mWater = Q/(cWater*differenceInTemp)
volumeWater = mWater/densityWater;
maxFlowWater = volumeWater/(time*60);

The Attempt at a Solution


differenceInTemp = 95 - 45
work = 45000
time = 24
energy = work*time
(This is the energy used by the water heater)
cWater = 1
The energy used by the water heater is equal to the energy received by the water, so: energy = Q = mWater*cWater*differenceInTemp

mWater = energy/(cWater*differenceInTemp);
densityWater = 62.428;
volumeWater = mWater/densityWater;

maxFlowWater = volumeWater/(time*60);

I was told there was a problem with my formula, but I can't find it.
 
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  • #2
By "heat capacity" am I right to assume you are using "specific heat capacity"? I'm assuming you're right with the constants - imperial units are pretty alien to me hahaha

Also, in your very last step (funding flow rate), I think the "error" came about when you divided by (time*60) - there seems to be no reason to have an additional "time" in there (dividing by 60 minutes will do, since it's what you're looking at to find cubic metres per minute).
 
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  • #3
Alloymouse said:
By "heat capacity" am I right to assume you are using "specific heat capacity"? I'm assuming you're right with the constants - imperial units are pretty alien to me hahaha

Also, in your very last step (funding flow rate), I think the "error" came about when you divided by (time*60) - there seems to be no reason to have an additional "time" in there (dividing by 60 minutes will do, since it's what you're looking at to find cubic metres per minute).
I'm bad with imperial units too, they do not make any sense to me. I was just asked to use them, so I'm just 80% sure about the values.
I multiplied the time by 60 to get the flow in cubic feet per minutes, rather than cubic feet per hour. I understood that I was computing the energy for 24 hours, so I should divide it back to one hour, then one minute.
 
  • #4
frequentPeriod said:
I'm bad with imperial units too, they do not make any sense to me. I was just asked to use them, so I'm just 80% sure about the values.
I multiplied the time by 60 to get the flow in cubic feet per minutes, rather than cubic feet per hour. I understood that I was computing the energy for 24 hours, so I should divide it back to one hour, then one minute.

Ah, understood.

Hmmm can't find anything else that might cause and error. Have you used your formulae to work things out? If so, what is the correct answer?
 
  • #5
I think the results should be reported in gallons per minute.
 
  • #6
Chestermiller said:
I think the results should be reported in gallons per minute.
The question did specify cubic feet per minute though
 
  • #7
Alloymouse said:
The question did specify cubic feet per minute though
True. But, in practice, home water flows are virtually always expressed in gpm.
 

FAQ: How Can You Calculate the Maximum Flow Rate for a Hot Shower?

What is a calorimetry hot shower problem?

A calorimetry hot shower problem is a scientific experiment that involves measuring the change in temperature of a substance, usually water, when it is heated by a hot shower. It is used to determine the amount of heat energy released by the shower and the efficiency of the shower system.

How is a calorimetry hot shower problem set up?

The experiment is typically set up by filling a container with a known amount of water and measuring its initial temperature. Then, the hot shower is directed into the container and the change in temperature of the water is measured. The container is usually insulated to prevent heat loss to the surroundings.

What are the main factors that affect the results of a calorimetry hot shower problem?

The main factors that affect the results of a calorimetry hot shower problem include the initial temperature of the water, the temperature and flow rate of the hot shower, and the insulating properties of the container. The accuracy of the temperature measurements and the calibration of the equipment used are also important factors.

What is the purpose of a calorimetry hot shower problem?

The purpose of a calorimetry hot shower problem is to determine the amount of heat energy released by a hot shower and to assess the efficiency of the shower system. This information can be used to make improvements to the system and to conserve energy.

What are the potential sources of error in a calorimetry hot shower problem?

Potential sources of error in a calorimetry hot shower problem include heat loss to the surroundings, inaccurate temperature measurements, and variations in the flow rate of the hot shower. It is important to control these factors as much as possible to ensure accurate results.

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