Question

(25 pts) Estimate how much collector area and storage capacity would be required for an active solar hot-water system designed to supply the total needs for two four-person families, one living in Manchester, New Hampshire, where the latitude is 44+o north and the other in Albuquerque, New Mexico, at 35+o North. The heat capacity of water is about 4200 J/kgoC and the hot water supply temperature in both houses is 60oC (140oF). State and justify all additional assumptions made.

Answer 1

The required total area is 1.48 m²

Step-by-step explanation:

Given that,

Latitude = 44+° N

New Mexico,

Latitude= 35+° N

Heat capacity = 4200 J/Kg°C

Temperature = 60°C

Let us assume the input temperature 22°C

Estimate volume of water 100 ltr for 4 person.

We need to calculate the heat

Using formula of heat

`H=mc_(p)\Delta T`

`H=mc_(p)(T_(f)-T_(i))`

Put the value into the formula

`H=100*4200*(60-22)`

`H=15960\ KJ`...(I)

Let solar radiation for 6 hours/day.

We need to calculate the total energy per unit area

Using formula of energy

`E=1000*6*3600\ J/m^2`

`E=21600\ KJ/m^2`

Let the efficiency of collector is 50 %

Then, the total energy per unit area will be

`E=21600*(50)/(100)`

`E=10800\ KJ/m^2`....(II)

We need to calculate the required total area

Using equation (I) and (II)

`A=(H)/(E)`

Where, H = heat

E = total energy

Put the value into the formula

`A=(15960)/(10800)`

`A=1.48\ m^2`

Hence, The required total area is 1.48 m²