# Stagnation pressure across a normal shock wave

• Ali Baig
In summary, the body entering the Earth's atmosphere at a Mach number of 20 is subjected to a normal shock wave and an ambient temperature of 220 K. The stagnation pressure and temperature at the nose of the body can be determined using the perfect gas law and isentropic flow equations.
Ali Baig
A body is reentering the Earth's atmosphere at a Mach number of 20. In front of the body is a shock
wave. Opposite the nose of the body, the shock can be seen to be normal to the flow direction. Determine the stagnation pressure and temperature to which the nose is subjected. Assume that the air behaves as a perfect gas (neglect dissociation) with constant γ = 1.4. The ambient pressure and temperature are equal to 1.0 kPa and 220 K.

I know all the relevant equations. My question is what is meant by ambient temperature. Does it mean static or stagnation pressure of the free stream?

The ambient temperature refers to the temperature of the air surrounding the body. In this case, the ambient temperature is given as 220 K. The stagnation pressure and temperature to which the nose is subjected can be calculated using the perfect gas law and the isentropic flow equations.

## 1. What is stagnation pressure?

Stagnation pressure is the maximum pressure that a fluid can reach when it is brought to a complete stop, also known as stagnation. This pressure is a combination of the dynamic pressure (pressure due to fluid motion) and the static pressure (pressure due to the weight of the fluid).

## 2. How is stagnation pressure affected by a normal shock wave?

A normal shock wave is a sudden and intense increase in pressure and temperature that occurs when a fluid flows at supersonic speeds and encounters an obstacle. Across the shock wave, there is a significant decrease in stagnation pressure due to the conversion of kinetic energy into thermal energy, resulting in a decrease in the total pressure of the fluid.

## 3. What factors affect the magnitude of stagnation pressure across a normal shock wave?

The magnitude of stagnation pressure across a normal shock wave is affected by the Mach number (speed) of the fluid, the angle of the shock wave, and the properties of the fluid, such as its temperature and molecular weight. A higher Mach number or a larger angle of the shock wave will result in a greater decrease in stagnation pressure.

## 4. How is stagnation pressure measured in a normal shock wave?

Stagnation pressure can be measured using a Pitot tube, which is a small tube with two openings - one facing the oncoming flow and one facing away from the flow. The difference in pressure between the two openings is equal to the stagnation pressure. Another method is using a pressure transducer, which converts the pressure into an electrical signal that can be measured.

## 5. What are the practical applications of understanding stagnation pressure across a normal shock wave?

Understanding stagnation pressure across a normal shock wave is important in the design of supersonic and hypersonic aircraft, as well as in the study of high-speed fluid dynamics. It is also relevant in the design of gas turbine engines, where the efficiency and performance are affected by the changes in stagnation pressure across the compressor and turbine stages.

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