Calculating Speed of Sound at Inlet

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Discussion Overview

The discussion revolves around the calculation of the speed of sound in air flowing through a nozzle, specifically addressing whether to use static or stagnation temperature for this calculation. The context includes theoretical considerations related to fluid dynamics and thermodynamics in nozzle flow.

Discussion Character

  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant suggests using the formula for the speed of sound in an ideal gas, c = sqrt(k * R * T), but questions whether to use static or stagnation temperature for the calculation.
  • Another participant inquires about which sonic velocity should be used for calculating the Mach number at the inlet, also questioning the relevance of static versus stagnation temperature.
  • A third participant notes that at the inlet of a De Laval nozzle, the air speed is sub-sonic, and that the flow becomes choked at the nozzle's narrowest point, where the velocity increases.
  • This participant provides an equation for calculating the exhaust velocity at the nozzle exit, emphasizing the use of static temperature in the context of their explanation.
  • A later reply confirms that the equation mentioned references the static temperature.

Areas of Agreement / Disagreement

Participants express differing views on whether static or stagnation temperature should be used for calculating the speed of sound and Mach number, indicating that the discussion remains unresolved.

Contextual Notes

There are limitations regarding the assumptions made about the flow conditions and the definitions of static and stagnation temperatures, which are not fully explored in the discussion.

jason.bourne
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suppose air is flowing through the nozzle
with the inlet conditions
static pressure = .2 MPa
static temperature = 350 K
velocty of air at the inlet = 150 m/s

speed of sound for ideal gas is given by c = sqrt (k * R * T)

suppose if i want to calculate the speed of sound at the inlet do i have to consider the static temperature or the stagnation temperature?
 
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i mean suppose if we want to calculate the mach number at the inlet, then which sonic velocity has to be used? is it the sonic velocity based on static temperature or the stagnation temperature?
 
you are talking about De Laval nozzle , at the inlet the speed of air is not sonic it is sub-sonic and when it enters at the tightest point in nozzle where the flow is choked and then the velocity incease at the end of the nozzle which is divergeant

velocit calculated at outlet is :
Ve=radica{(T.R/M).(2K/K-1).[1-(Pe/p)^k-1/k]}

Ve = Exhaust velocity at nozzle exit, m/s
T = absolute temperature of inlet gas, K
R = Universal gas law constant = 8314.5 J/(kmol·K)
M = the gas molecular mass, kg/kmol (also known as the molecular weight)
k = cp/cv = isentropic expansion factor
cp = specific heat of the gas at constant pressure
cv = specific heat of the gas at constant volume
Pe = absolute pressure of exhaust gas at nozzle exit, Pa
P = absolute pressure of inlet gas, Pa

http://en.wikipedia.org/wiki/De_laval_nozzle
 
Jason,
That equation references the static temperature.
 

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