Find (D V / D t) for the system in Problem 4.64. Problem 4.64 Figure P4.64 shows
Question:
Find \(D V / D t\) for the system in Problem 4.64.
Problem 4.64
Figure P4.64 shows a fixed control volume. It has a volume \(V_{0}=1.0 \mathrm{ft}^{3}\), a flow area \(A=1.0 \mathrm{ft}^{2}\), and a length \(\ell_{0}=1.0 \mathrm{ft}\). Position \(x\) represents the center of the control volume where the fluid velocity \(V_{0}=1.0 \mathrm{ft} / \mathrm{s}\) and the density \(ho_{0}=1.800 \mathrm{slug} / \mathrm{ft}^{3}\). Also, at position \(x\) the fluid density does not change locally with time but decreases in the axial direction at the linear rate of \(0.25 \mathrm{slug} / \mathrm{ft}^{4}\). Use the system or Lagrangian approach to evaluate \(d p / d t\). Compare this result with that of the material derivative and flux terms.
Figure P4.64
Step by Step Answer:
Munson Young And Okiishi's Fundamentals Of Fluid Mechanics
ISBN: 9781119080701
8th Edition
Authors: Philip M. Gerhart, Andrew L. Gerhart, John I. Hochstein