Calculating Speed of Sound at Inlet

In summary, the De Laval nozzle is a type of nozzle used in rocket engines to accelerate the flow of a gas (in this case, air). The speed of sound for an ideal gas is given by the equation c = sqrt (k * R * T), where k is the isentropic expansion factor, R is the universal gas law constant, and T is the absolute temperature. To calculate the speed of sound at the inlet, the static temperature is used. When calculating the Mach number at the inlet, the sonic velocity based on the static temperature is used. The De Laval nozzle has a sub-sonic speed at the inlet, but as the flow enters the tightest point in the nozzle, it becomes choked and the velocity
  • #1
jason.bourne
82
1
suppose air is flowing throught 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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  • #2
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?
 
  • #3
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
 
  • #4
Jason,
That equation references the static temperature.
 

FAQ: Calculating Speed of Sound at Inlet

What is the speed of sound at inlet?

The speed of sound at inlet, also known as the inlet Mach number, is the velocity at which sound travels through the inlet of a fluid flow system. It is typically measured in meters per second or feet per second.

How is the speed of sound at inlet calculated?

The speed of sound at inlet can be calculated using the formula: Mach number = inlet velocity / speed of sound. The speed of sound can vary depending on factors such as temperature, humidity, and altitude.

Why is it important to calculate the speed of sound at inlet?

Calculating the speed of sound at inlet is important in fluid dynamics and aerodynamics, as it helps engineers and scientists understand the behavior of fluids and gases in different flow systems. It is also crucial in the design and operation of various machines and vehicles, such as aircrafts and rockets.

What are the units of measurement for the speed of sound at inlet?

The speed of sound at inlet is typically measured in units of velocity, such as meters per second or feet per second. However, it can also be expressed in terms of Mach number, which is a dimensionless quantity.

How does temperature affect the speed of sound at inlet?

Temperature affects the speed of sound at inlet because sound travels faster in warmer air compared to colder air. This is because warmer air molecules have higher kinetic energy, allowing them to vibrate more quickly and transmit sound waves faster. Therefore, the speed of sound at inlet increases as temperature increases.

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