Find the Mass Flow Rate Through the Nozzle

In summary, we are given information about helium gas flowing through a well-insulated nozzle at steady state. The temperature and velocity at the inlet are 550°R and 150 ft/s, respectively, while at the exit, the temperature is 400°R and the pressure is 40 lbf/in2. The area of the exit is 0.0085 ft2. Using the ideal gas model with k = 1.67 and neglecting potential energy effects, we need to determine the mass flow rate in lb/s through the nozzle. To solve this, we can use the equation m' = ρvA, where ρ is the density, v is the velocity, and A is the area. We also
  • #1
Northbysouth
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Homework Statement


Helium gas flows through a well-insulated nozzle at steady state. The temperature and the velocity at the inlet are 550°R and 150 ft/s, respectively. At the exit, the temperature is 400°R and the pressure is 40 lbf/in2. The area of the exit is 0.0085 ft2. Using the ideal gas model with k = 1.67, and neglecting potential energy effects, determine the mass flow rate in lb/s through the nozzle


Homework Equations





The Attempt at a Solution



My initial response is to use:

m' = ρvA

but I'm not sure if this is how they want me to find the answer. My professor mentioned:

Cp - Cc = R

Is this referring to specific heats?

My notes also say Cp is constant. What is this referring to? Likewise, what is the significance of the k=1.67?
 
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  • #2
k is the ratio of specific heats of the gas:

k = Cp/Cv
 
  • #3
What is the significance of giving me the ratio of the specific heats of the helium?
 

1. What is mass flow rate and why is it important?

Mass flow rate is the amount of mass that passes through a given cross-sectional area per unit time. It is an important parameter in fluid dynamics as it helps us understand the rate at which a fluid is flowing and how much mass is being transported. It is especially important in nozzle design as it affects the performance and efficiency of the nozzle.

2. How is the mass flow rate through a nozzle calculated?

The mass flow rate through a nozzle can be calculated using the equation: m_dot = rho * A * V, where m_dot is the mass flow rate, rho is the density of the fluid, A is the cross-sectional area of the nozzle, and V is the velocity of the fluid.

3. What factors affect the mass flow rate through a nozzle?

The mass flow rate through a nozzle is affected by the fluid properties such as density, viscosity, and compressibility. The geometry and size of the nozzle, as well as the pressure and temperature of the fluid, also play a role in determining the mass flow rate.

4. How does the mass flow rate through a nozzle impact the performance of a system?

The mass flow rate through a nozzle is directly related to the thrust produced in a propulsion system. In other systems, such as pumps and turbines, the mass flow rate affects the power output. A higher mass flow rate can also lead to increased heat transfer, which can impact the overall efficiency of the system.

5. How can the mass flow rate through a nozzle be controlled?

The mass flow rate through a nozzle can be controlled by adjusting the nozzle geometry, such as the shape and size of the throat and exit, and the fluid properties, such as temperature and pressure. Changing the operating conditions, such as the inlet pressure and temperature, can also have an impact on the mass flow rate through the nozzle.

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