This problem is in the text that is on cramster. The solution is not however. I

Question

This problem is in the text that is on cramster. The solution is not however. I do not know how to relate the temperature to the energy equation. There is a picture in the text of a house. water pipe into the house goes through a water meter then splits. One section goes to hot water heater and then to 2nd floor. This pipe goes to a dishwasher on the second floor then onto the shower. The other pipe carries cold water to the shower on the second floor.
Problem statement:
As shown is fig 8.114, cold water (T=50F)flows from the water meter to either the shower or the hot water heater. In the hot water heater it is heated to a temperature of 150F. Thus, with equal amounts of hot and cold water, the shower is at a comfortable 100F. However, when the dishwasher is turned on, the shower water becomes too cold. Indicate how you would predict the new shower temperature (assume the shower faucet is not adjusted). State any assumptions needed in your analysis.
I rate very high, Please help.

Explanation / Answer

To analyze you would need to assume that 1) the dishwasher is using only hot water and 2) the dishwasher cuts the amount of hot water going to the shower by half.

Right now, the amount of hot and cold water are equal, and the temp is 100°F. If you wanted to set up and equation for temp, you could show 50°(x) + 150°(y) = 100°, where x and y are the proportion of cold and hot water respectively. With each at 50%, we have 50(.5) + 150(.5) = 100. When the dishwasher takes half of the hot water away, the temp will drop. But when half of the water is taken, that doesn't mean more cold water is coming so you have to compensate. if X + Y = Total amt of water (lets say 100 to make it easy) we HAD 50 + 50 = 100. But now that we took half the hot water we have 50 + 25 = 75. The new proportion of cold water is 2/3 and the hot is 1/3. So now we have 50(2/3) + 150(1/3) = ??? Do the math, and I'd guess the new shower temp is about 83°F

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.