This is just prep for a paper I have to write. Please ignore the post. If you are interested it’s for a heat exchanger experiment we did with old equipment and temperature sensors with an uncertainty greater than the difference we were trying to measure. Don’t worry, our stadium was just redone with brick.

$\frac{P_1}{\rho} + \frac{1}{2} V_1^{2} = \frac{P_2}{\rho} + \frac{1}{2} V_2^{2}$

$\Huge{C_c = (\dot{m} c_p )_c} \textup{(Eq. 1)}$

$C_h = (\dot{m} c_p )_h \textup{(Eq. 2)}$

$C_r = \dfrac{C_{min}}{C_{max}} \textup{(Eq. 3)}$

$q_c = C_c (T_{co} - T_{ci}) \textup{(Eq. 4)}$

$q_h = C_h (T_{hi} - T_{ho}) \textup{(Eq. 5)}$

$q = \dfrac{q_c + q_h}{2} \textup{(Eq. 6)}$

$q_{max} = C_{min} (T_{hi} - T_{ci}) \textup{(Eq. 7)}$

$\epsilon = \dfrac{q}{q_{max}} \textup{(Eq. 8)}$

$\epsilon = q/{q_{max}} \textup{(Eq. 9)}$

$q = U A \Delta T_{lm} \textup{(Eq. 10)}$

$\Delta T_{lm,CF} =\dfrac{\Delta T_1 - \Delta T_2}{\ln{\dfrac{\Delta T_1}{\Delta T_2}}} \textup{(Eq. 11)}$

$\Delta T_{lm,CF} =\frac{\Delta T_1 - \Delta T_2}{\ln{\frac{\Delta T_1}{\Delta T_2}}} \textup{(Eq. 12)}$

$\Delta T_{lm,CF} =\dfrac{\Delta T_1 - \Delta T_2}{\ln{\frac{\Delta T_1}{\Delta T_2}}} \textup{(Eq. 13)}$

$\Delta T_1 = T_{hi} - T_{co} \textup{(Eq. 14)}$

$\Delta T_2 = T_{ho} - T_{ci} \textup{(Eq. 15)}$

$\Delta T_{lm} = F \Delta T_{lm,CF} \textup{(Eq. 16)}$

$NTU = \dfrac{U A}{C_{min}} = \textup{(Eq. 16)}$

$F = m a \textup{(Eq. 1)}$

$\textbf{F = m a} (Eq. 1)$

$\textmd{F = m a} (Eq. 1)$