The following pressures for the air flow in Problem 4.24 were measured:

Find the local rate of change of pressure \(\partial p / \partial t\) and the convective rate of change of pressure \(V \partial p / \partial x\) at \(t=2.0 \mathrm{~s}\) and \(x=10 \mathrm{~m}\).

Problem 4.24

Air is delivered through a constant-diameter duct by a fan. The air is inviscid, so the fluid velocity profile is "flat" across each cross section. During the fan start-up, the following velocities were measured at the time \(t\) and axial positions \(x\) :

Calculate the local acceleration, the convective acceleration, and the total acceleration at \(t=1.0 \mathrm{~s}\) and \(x=10 \mathrm{~m}\). What is the local acceleration after the fan has reached a steady air flow rate?

Transcribed Image Text:

x = 0 x = 10 m x = 20 m 1=0s t = 1.0 s p = 101 kPa p = 101 kPa p = 101 kPa p = 121 kPa p = 116 kPa p = 111 kPa t = 2.0 s p = 141 kPa p = 131 kPa p = 121 kPa t = 3.0 s p = 171 kPa p = 151 kPa p = 131 kPa.