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Bernoulli Equation Applications (pp. 220-232)

Recall from last time the equation of

• steady ($\frac{\partial}{\partial t} = 0$)

• inviscid ($\frac{\partial V}{\partial y} = 0$)

• gravity vector is down ($-z$)

• incompressible ($\rho = constant$)

• irrotational ($curl(V)=0$)

Results in

$\frac{p_1}{\rho g} + \frac{V_1^2}{2g} + z_1 = \frac{p_2}{\rho g} + \frac{V_2^2}{2g} + z_2$

Below are some examples illustrating its use

Example: Flow out of a holy tank

Identify the problem solving steps employed

Example: Pressure near tank outlet

Identify the problem solving steps employed

Example: How high will a fountain go?

Consider the fountains at a resort. What kind of pressures and velocities are required to make the show happen?

Here’s a related problem that could form the basis of fountain design.

Identify the problem solving steps employed

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Fluid Rotation and Vorticity (pp. 336-354)

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Rotation of a Fluid (pp. )