Consider an isentropic flow of air (ratio of specific heats $=1.4$ ) through a duct as shown in the figure.
The variations in the flow across the cross-section are negligible. The flow conditions at Location $1$ are given as follows:
$$P_1=100 \; \mathrm{kPa}, \rho_1=1.2 \mathrm{~kg} / \mathrm{m}^3, u_1=400 \mathrm{~m} / \mathrm{s}$$
The duct cross-sectional area at Location $2$ is given by $A_2=2 A_1$, where $A_1$ denotes the duct cross-sectional area at Location $1.$ Which one of the given statements about the velocity $u_2$ and pressure $P_2$ at Location $2$ is $\text{TRUE?}$
- $u_2<u_1, P_2<P_1$
- $u_2<u_1, P_2>P_1$
- $u_2>u_1, P_2<P_1$
- $u_2>u_1, P_2>P_1$