Calculate Acceleration at A, B and C in Fluid Flow Through Venturi Cone

[Varidius]

Fluid is flowing through a venturi-like cone, 0.1m long, horizontally along a streamline. At the start, it is traveling at 6m/s and after 0.1m it is traveling at 18m/s. Velocity is also stated to be a linear function of distance along the streamline. The question asks to determine the acceleration at at the point where it is 6m/s (A), at the point where it is 18m/s (B) and at a distance halfway between (C).

Since the problem says that velocity is linear with distance, I feel safe in saying that nothing too weird happens in between and basic physics apply (no crazy decelerations).

I'm thinking of using basic physics equations (ie. that use starting velocity, resultant velocity, displacement and acceleration) and solving for acceleration for each leg (A-C, C-B), but that'll only give me two acceleration values.

How do I solve this?

 

[Delta2]

Velocity linear with distance means that velocity $$v=v_A+cs$$ where $$v_A=6m/s$$. We know that for $$s=0.1, v_B=18$$ hence we can find
$$c=\frac{v_B-v_A}{s}=120$$

Use the fact that velocity is linear with distance to prove that acceleration is linear with velocity more specifically that $$a=cv=120(6+120s)$$.

 

[Varidius]

Sorry, stupid question, but what's c?

 

[Delta2]

It is just the constant of the linear relationship that velocity has with distance. It is also called the slope or gradient.

Problem states that velocity is a linear function of distance, which means that there are constants b and c such that $$v=b+cs$$. If we plot this equation on a diagram with velocity v on vertical axis and distance s on horizontal axis then what we get is a line, hence the word linear.

Check http://en.wikipedia.org/wiki/Linear_equation