I Explain Bernoulli at the molecular level?

[erobz]

Lets assume that the flow in the control volume is uniformly distributed, and experiences a constant acceleration along the circular arc $s$.

In other words $\ddot s = k$ implies:

$$ \frac{d \dot s }{d \theta} \frac{d \theta }{dt} = k $$

Since $\dot s = r \dot \theta$:

$$ \frac{d \dot s }{d \theta} \frac{\dot s }{r} = k $$

Separate variables, integrate this over $\theta$, with $\dot s = V$ implies that the scalar velocity of the flow along at any point along the arc is given by:

$$ V = \sqrt{2kr \theta + V_1^2} $$

Does anyone have complaints about the "lever pulling" I'm about to do for fear of basic representation of the unsteady terms in the Mass Continuity/ Energy equations before I go further?

I believe I can get the pressure $P_2$ at the outlet as function of $V_1, \dot V_1, k$ etc... (the velocity of the cart, cart acceleration, etc... ). Explicitly I'm not sure, but at least implicitly it looks like I have it.

 

[Lnewqban]

I agree. I'm waiting to see if someone wants to move all the glider related posts to another thread. If they just want to delete them, I wouldn't have an issue with that either, but don't know about the others involved. I did go through and did strike-through on my prior posts.

Paging @berkeman and @russ_watters.