Calculating Acceleration Along Streamline XY=4: Problems at Point B?

In summary, the conversation is discussing the calculation of acceleration at different points on a streamline. The lecturer notes that at point A, the fluid is decelerating, at point B, the acceleration is zero, and at point C, it is accelerating. However, there is an issue with the calculation at point B. The first method used to calculate acceleration at point B does not result in zero acceleration, while the second method does. The difference between these two methods is not clear. Additionally, there is a question about the meaning of a linear change in cross-sectional area in a nozzle and the values of velocity components u, v, and V.
  • #1
tommywan410
5
0
Along a streamline xy = 4, given u = 2x, v = -2y,
I was trying to calculate the acceleration at three different points A(1,4), B(2,2), C(4,1),
In my lecture notes, it is said that at A, the fluid is decelerating, at B, the acceleration is zero, and at C it is accelerating. However, i got some problem with my calculation at B.
V=ui+vj therefore the a = 4xi+4yj, when i plug in B, the acceleration is not zero. Why would it happen? Is there any problems with my calculation?

If i use another approach (i am not sure), V = sqrt(u^2+v^2), then
a = 2(u^2-v^2)/sqrt(u^2+v^2), when i plug in B, it is zero now. What is the difference between these two methods?


Another question is that in one of my practice problems, it is said that in a nozzle the cross-sectional area changes linearly from the base to the tip, does it mean that
A = A(in) + kx, where A is the cross-sectional area x m away from the inlet?
 
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  • #2
What is V, u,v ?
 
  • #3
ajayguhan said:
What is V, u,v ?
Big V is the velocity vector. V=ui+vj+wk, where i,j, and k are unit vectors in the x y and z directions.
 

1. What is acceleration along streamline XY=4?

Acceleration along streamline XY=4 is the rate of change of velocity with respect to time at a specific point on the streamline. It measures the change in speed and direction of a fluid particle as it moves along the streamline.

2. How do you calculate acceleration along streamline XY=4?

To calculate acceleration along streamline XY=4, you need to first determine the velocity at the point on the streamline (point B). Then, you can use the formula a = dv/dt, where a is the acceleration, dv is the change in velocity, and dt is the change in time.

3. What are some problems that can occur at point B when calculating acceleration along streamline XY=4?

One problem that can occur at point B is if the streamline intersects with a solid object, causing a sudden change in direction and velocity. Another problem could be if the fluid flow is turbulent, making it difficult to accurately measure the velocity at point B.

4. How can you account for variations in velocity when calculating acceleration along streamline XY=4?

To account for variations in velocity, you can take multiple measurements at different points along the streamline and calculate the average velocity. This will provide a more accurate representation of the fluid particle's speed and direction at point B.

5. Why is calculating acceleration along streamline XY=4 important in fluid mechanics?

Calculating acceleration along streamline XY=4 allows us to better understand the behavior of fluids and their interactions with solid objects. It can help us predict the movement of fluids, such as in weather patterns or in the design of water systems. It is an important tool in fluid mechanics for analyzing and solving real-world problems.

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