Question #43762

A large reservoir maintained at a constant pressure $P_0 \text{ (N/m}^2\text{)}$ drives an ideal, incompressible fluid of density $\rho \text{ (kg/m}^3\text{)}$ through a horizontal pipe of uniform cross-sectional area $A \text{ (m}^2\text{)}$ and length $L \text{ (m)}$. The fluid discharges into the atmosphere at pressure $P_{\text{atm}} \text{ (N/m}^2\text{)}$. Initially, the exit aperture has an area $A$, and the fluid flows steadily with a velocity $v_0 \text{ (m/s)}$. At $t=0 \text{ s}$, a dynamic mechanism instantaneously constricts the exit aperture to an area $A/2$. The length of the constricted section is negligible. What is the magnitude of the instantaneous acceleration $\text{(m/s}^2\text{)}$ of the fluid column in the pipe immediately after the constriction at $t=0^+$?