# Question: in the infinitesimal neighborhood of a point in an inviscid...

###### Question details

In the infinitesimal neighborhood of a point in an inviscid flow, the small change in pressure corresponding to a change in velocity is given by .

- Using this relation, derive a differential relation for the fractional density as a function of the fractional change in velocity with the compressibility as a coefficient.
- The velocity in a point in isentropic flow of air is 10m/s (a
low speed flow) and the density and pressure are 1.23
kg/m
^{3}and 1.01x10^{5}N/m^{2}. The fractional change in velocity is 0.01. Calculate the fractional change in density. - Repeat part (b) except for a local velocity of 1000m/s (a high speed flow). Compare this result with that of part (b) and comment on the differences.