Question

Q1. Pressure load in re-entry capsule nose A crew capsule has re-entered Earths atmosphere and slowed to a speed of V-1134 m/s at an altitude where the static temperature is T-200 K and the static pressure is p=1 kPa. A normal shock forms upstream of the nose of the capsule. What is the pressure of the flow where it stagnates against the nose of the capsule? Assume the air behaves as a calorically perfect gas with ratio of specific heats γ : 1.4 and gas constant R-287 J/kg/K.

Answer 1

Given

Speed of Crew Capsule =1134 m/s

Static Temperature =200K

Static Pressure $P_{static}$ =1kPa

ratio of Specific heats is 1.4

gas constant =287 J/kg/K

Here we are asked to calculate pressure of the flow where it stagnates the nose of capsule

that means we have to stagnation pressure

$P_{stagnation} = \frac{1}{2}\rho v^{2}+P_{static}$ .........................(1)

where $\rho -$ Density of Fluid (Here Air)

   Velocity

from ideal gas equation $PV=mRT\Rightarrow P=\rho RT$

so $\rho =\frac{P}{RT}=\frac{1\times 10^{3}}{287\times 200}=0.0174(kg/m^{3})$

substituting values in equation (1)

$P_{stagnation} = \frac{1}{2}(0.0174)( 1134^{2})+1\times 10^{3}$

therefore pressure of the flow where it stagnates the nose of the capsule is 12.187kPa