As is indicated in Fig. P4.42, the speed of exhaust in a car's exhaust pipe varies in

Question:

As is indicated in Fig. P4.42, the speed of exhaust in a car's exhaust pipe varies in time and distance because of the periodic nature of the engine's operation and the damping effect with distance from the engine. Assume that the speed is given by $V=V_{0}\left[1+a e^{-b x} \sin (\omega t)\right]$, where $V_{0}=8 \mathrm{fps}, a=0.05$, $b=0.2 \mathrm{ft}^{-1}$, and $\omega=50 \mathrm{rad} / \mathrm{s}$. Calculate and plot the fluid acceleration at $x=0,1,2,3,4$, and $5 \mathrm{ft}$ for $0 \leq t \leq \pi / 25 \mathrm{~s}$.

Figure P4.42