Duct Flow

$$\epsffile{figures/duct.ps}$$

Assumptions: $h_1>h_2$. The reservoirs are wide enough that the flow is quasi-steady. The two reservoirs have the same width, so that $V_1=V_2$.

Bernoulli:

$$p_1 + {\textstyle\frac{1}{2}} \rho V_1^2 + \rho g h_1 = p_2 + {\textstyle\frac{1}{2}} \rho V_2^2 + \rho g h_2$$

Since $p_1=p_2=p_a$ and $V_1=V_2$:

$$\rho g h_1 = \rho g h_2$$

hence $h_1=h_2$.

Exercise:

What is wrong in this analysis?

1. Is $p_1=p_2=p_a$ correct?
2. Is $V_1=V_2$ correct?
3. When does the Bernoulli law apply?
4. How about the energy balance?
5. Is the Bernoulli law the correct one?
6. Is the length of the connecting duct AD important?

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