Reduction of velocity in an isentropic process?

[hanson]

Hi all.
We are to compare the effect of a shock wave, that is the irreversibilities associated.
We have comptued that the upstream and downstream velocities of a shock wave are 1029 m/s and 266.8 m/s respectively.
The upstream pressure and temperature is 105kPa and 290K.
What question proceed to ask that what would be the pressure if the velocity had been reduced isentropically from the initial velocity to that behind the shock.

How would you compute it?
I use the continuity equation to work out the ratio between upstream and downstream densities.
Then use the isentropic relation p/(roll^gamma)=constant to compute the pressure. But it turns out I am wrong.

Can anyone help? And also tell me why I am wrong? Thanks.

 

[LightHero]

For this problem, you cannot use the continuity equation since the shock wave is not an isentropic process. The pressure behind the shock wave is determined by the Rankine-Hugoniot relations, which describe the behavior of a shock wave. Instead of using the continuity equation, you should use the Rankine-Hugoniot relations to calculate the pressure behind the shock.

 

[astrokreng]

The reduction of velocity in an isentropic process is a common occurrence in thermodynamics and fluid mechanics. In an isentropic process, the entropy remains constant, meaning there is no heat transfer or friction present. This often occurs in idealized systems or in adiabatic processes.

In the case of a shock wave, the reduction of velocity is due to the sudden increase in pressure and temperature. This results in an increase in density, which in turn causes a decrease in velocity according to the continuity equation. However, this reduction in velocity is not an isentropic process because there is a transfer of kinetic energy into heat due to the shock wave.

To compute the pressure in this scenario, you would need to consider the energy equation, taking into account the energy lost due to the shock wave and the resulting increase in temperature. This would give you a more accurate calculation of the pressure behind the shock.

It is important to note that the isentropic relation you used, p/(rho^gamma)=constant, only applies in isentropic processes and is not applicable in the case of a shock wave. This is why your calculation did not yield the correct result.

I hope this explanation helps and clarifies why your calculation was incorrect. In general, it is always important to consider all relevant equations and factors when solving a problem in science, and to be aware of the limitations and assumptions of certain equations and models.