QUESTION $2$

$2\mathrm{.}1$ The storage size $V_{\text{s}\text{t}\text{o}\text{r}\text{a}\text{g}\text{e}}$ for domestic hot water is twice the total requirements of persons $(P)$ with a daily requirement $V_{\text{p}\text{e}\text{r}\text{s}\text{o}\text{n}}$ per person.

Based on the hot water requirement $Q_{\text{p}\text{e}\text{r}\text{s}\text{o}\text{n}}$ per person per day, for a four$-$person household with an average consumption of $45$ litres or $1\mathrm{.}8$ kWh of hot water per day,

$($a$)$ calculate the storage size $V_{\text{s}\text{t}\text{o}\text{r}\text{a}\text{g}\text{e}}$ in litres

$($b$)$ the annual hot water requirement $Q_{hw}$ in kWh

$($c$)$ If the annual solar radiation is $H_{\text{s}\text{o}\text{l}\text{a}\text{r}}=1000\frac{kWh}{m^2},$ annual solar fraction $s_f=0\mathrm{.}9,$ tilt gains $f_{\text{o}\text{r}\text{i}\text{e}\text{n}\text{t}\text{a}\text{t}\text{i}\text{o}\text{n}}=110\%$ and collector efficiency is ${}_c=30\%,$ using the relationship below, calculate the collector size

$A_c=\frac{s_f{Q}_{hw}}{{}_c{H}_{\text{s}\text{o}\text{l}\text{a}\text{r}}{f}_{\text{o}\text{r}\text{i}\text{e}\text{n}\text{t}\text{a}\text{t}\text{i}\text{o}\text{n}}}$

$($d$)$ If the effective area of this solar panel in $2\mathrm{.}1($c$)$ is $0\mathrm{.}8\frac{m^2}{?}$ piece, estimate the number of pieces of solar panel that should be installed to collect this heat demand.

$2\mathrm{.}2($a$)$ If this family with $4$ members plans to install a solar water heater which is mainly used for bath and the hot$-$water temperature required for bath is $50C,$ while the annual average temperature of cold water is $23C,$ estimate the heat that should be provided by the solar water heater to satisfy the family's demand for bath.

$3$

$($b$)$ If there is a certain solar panel with effective area of $0\mathrm{.}8\frac{m^2}{?}$ piece which can offer a heat supply of $7200k\frac{J}{m^2}$ in a day, estimate the required installation area of the solar panel and the number of pieces needed.

$(2)$