- #1

Master1022

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- Homework Statement
- General problem. For example, air enters a wind tunnel (or a jet; basically something that has a larger area of entry than exit) and the total pressure is atmospheric pressure. Write out the momentum equation for this control volume.

- Relevant Equations
- Bernoulli's Equation

Momentum Equation

So if we define point 1 at the entrance and point 2 at the exit, then we can write out Bernoulli's equation along a horizontal streamline as such: [tex] p_1 + \frac{1}{2}\rho v_{1}^2 = p_2 + \frac{1}{2}\rho v_{2}^2 = p_{atm} [/tex]

One question is:

Then later on, when we write the momentum equation for our control volume, we get (Force = Change in Momentum Flux R(-->)):

[tex] p_1 A_1 - p_2 A_2 - p_{atm}(A_1 - A_2) + F = \rho u_2 ^ 2 A_2 - \rho u_1 ^ 2 A_1 [/tex]

However, once again, I cannot understand why there isn't a p_atm term for A1 & A2?

Apologies for this, as I understand there is some basic error.

Thanks in advance

One question is:

**won't there be p_atm also contributing to the static pressure at p1 and p2 (i.e. p_atm + p_1 or p_atm + p_2)?**Mathematically I see that there would be problems if we had this in the equation, but I cannot understand why. Does atmospheric pressure not contribute to the static pressure inside an object (e.g. this wind tunnel or a pipe)?Then later on, when we write the momentum equation for our control volume, we get (Force = Change in Momentum Flux R(-->)):

[tex] p_1 A_1 - p_2 A_2 - p_{atm}(A_1 - A_2) + F = \rho u_2 ^ 2 A_2 - \rho u_1 ^ 2 A_1 [/tex]

However, once again, I cannot understand why there isn't a p_atm term for A1 & A2?

Apologies for this, as I understand there is some basic error.

Thanks in advance