Derive an equation for pressure loss of compressible $($air$)$ flow in a horizontal pipe, assuming

temperature $T$ as constant. Known values are: inlet pressure $p_1,$ outlet pressure $p_2,$ specific gas

constant $R,$ temperature $T,$ mass flow rate $q_m,$ pipe diameter $d,$ friction factor $f,$ pipe length $L$ and

the sum of local losses $K.$ Based on the equation you derived, choose the correct one from the

following.

Select one:

a$.\frac{p_1^2-p_2^2}{2}=RT\frac{8q_m^2}{{}^2{d}^5}(fL+dK)$

b$.\frac{p_1^2-p_2^2}{2}={}^2{d}^5\frac{8q_m^2}{RT}(fL+dK)$

C$.\frac{p_1^2-p_2^2}{2}=fL\frac{RT}{8q_m^2}({}^2{d}^5+dK)$

d$.\frac{p_1^2-p_2^2}{2}=fL\frac{dK}{RT}(8q_m^2+{}^2{d}^5)$

e$.\frac{p_1^2-p_2^2}{2}=dK\frac{8q_m^2}{RT}(fL+{}^2{d}^5)$

f$.\frac{p_1^2-p_2^2}{2}=8q_m^2\frac{{}^2{d}^5}{RT}(fL+dK)$

g$.\frac{p_1^2-p_2^2}{2}={}^2{q}_m^2\frac{RT}{8d^5}(fL+dK)$

h$.\frac{p_1^2-p_2^2}{2}=RT\frac{{}^2{d}^5}{8q_m^2}(fL+dK)$