GATE2015-1-47

Question

For flow through a pipe of radius $R$, the velocity and temperature distribution are as follows:
$u(r,x)=C_1,$, and $T(r,x)=C_2[1- \left (\dfrac{r}{R} \right )^3]$ where $C_1$ and $C_2$ are constants. The bulk mean  temperature is given by $T_m=\dfrac{2}{U_mR^2}\int_{0}^{R}u(r,x)T(r,x)rdr$, with $U_m$ being the mean velocity of flow. The value of $T_m$ is

• A. $\dfrac{0.5C_2}{U_m} \\$
• B. $0.5C_2 \\$
• C. $0.6C_2 \\$
• D. $\dfrac{0.6C_2}{U_m}$