Fluid Dynamics -- Find the maximum possible flow speed on the streamline....

In summary, the flow speed at point A is 100 m/s with a Mach number of 0.6. The maximum possible flow speed on the streamline through A is 345 m/s, and the flow speed at a point where the pressure has fallen to half its value at point A is yet to be determined. Bernoulli's equation for compressible flow and the Mach relations can be used to solve for this value.
  • #1
zigggy23
2
0

Homework Statement


At point A in the flow of a compressible fluid, the flow speed is 100 m s−1 and the Mach number of the flow is 0.6. Find (i) the maximum possible flow speed on the streamline through A, and (ii) the flow speed at a point where the pressure has fallen to half its value at point A. Assume the flow to be adiabatic, with index γ = 1.4

Homework Equations


bernoulli's equation for compressible flow & the mach relations

The Attempt at a Solution


I've done part a and I've been playing around with bernoulli's equation and the Mach relations found here https://www.grc.nasa.gov/www/k-12/airplane/isentrop.html for a few hours now. If anyone can help with part b would be much appreciated.
 
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  • #2
i) Maximum possible flow speed on the streamline through A:vmax = Ma * a = 0.6 * (γRT)^(1/2)= .6*(1.4*287*288)^(1/2) = 345 m/sii) Flow speed at point where pressure has fallen to half its value at point A:I'm stuck here
 

1. What is fluid dynamics?

Fluid dynamics is the study of how fluids (liquids and gases) behave and interact with each other and their surroundings. It involves understanding factors such as flow, pressure, and viscosity.

2. What is a streamline?

A streamline is an imaginary line that represents the path of a fluid particle as it moves through the fluid. It is used to visualize the flow of a fluid and can help determine the maximum possible flow speed.

3. How is the maximum possible flow speed on a streamline determined?

The maximum possible flow speed on a streamline is determined by analyzing the properties of the fluid, such as its viscosity and density, as well as the shape and size of the objects that the fluid is flowing around. This can be done through mathematical equations and computer simulations.

4. What factors affect the maximum possible flow speed on a streamline?

The maximum possible flow speed on a streamline can be affected by various factors including the shape of the object the fluid is flowing around, the viscosity of the fluid, the density of the fluid, and the velocity of the fluid at its entry point.

5. What is the significance of finding the maximum possible flow speed on a streamline?

Finding the maximum possible flow speed on a streamline is important in understanding and predicting how fluids will behave in different situations. It can help engineers design more efficient systems and structures, such as airplanes and pipelines, and can also aid in predicting weather patterns and ocean currents.

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