# Need help please with percentages, etc... for this real life Application

• Jul 29th 2011, 11:52 AM
TheyCallMeDave
Need help please with percentages, etc... for this real life Application
I have a solar hot water collector that puts out water at a very scalding 160 f . directly into the house hot water line ; My ideal water temperature for a shower is 95 f . If i mix in cooler water from my showers cold water faucet which delivers 75 f. during summer months , what percentage of Collector water (160 f) do I need to achieve a 95 f. shower ? If you would, please give me the mathematical formula by plugging in the values listed for the answer. I do appreciate it. Thanks, David.
• Jul 29th 2011, 12:03 PM
earboth
Re: Need help please with percentages, etc... for this real life Application
Quote:

Originally Posted by TheyCallMeDave
I have a solar hot water collector that puts out water at a very scalding 160 f . directly into the house hot water line ; My ideal water temperature for a shower is 95 f . If i mix in cooler water from my showers cold water faucet which delivers 75 f. during summer months , what percentage of Collector water (160 f) do I need to achieve a 95 f. shower ? If you would, please give me the mathematical formula by plugging in the values listed for the answer. I do appreciate it. Thanks, David.

1. The energy from the hot water is completely taken by the cold water:
$m_h$ = mass of hot water
$m_c$ = mass of cold water

2.
$m_h(160-95)=m_c(95-75)~\implies~\dfrac{m_h}{m_c}=\dfrac{20}{65}$

3. With 20 (liters, gallons, ...) of hot water and 65 (liters, gallons, ...) of cold water you'll get 85 (liters, gallons, ...) of water with the ideal temperature.
• Jul 29th 2011, 12:52 PM
bjhopper
Re: Need help please with percentages, etc... for this real life Application
Hi Dave,
I had a similar problem with a shower. My wife had a hard time adjusting temp so I installed a mixing valve and the hot water is controlled by the mix valve