Bernouilli’s Equation

This week we looked more into Bernouilli’s Equation. But to start off with, we had a quick ‘clicker’ quiz to recap on what we have learnt so far, and this highlighted some of the area I need to work on more.

Euler’s equation can be simplified when we integrate along streamlines, or when the flow is both inviscid and irrotational. In either case, we get a form of Bernouilli’s equation:

IMG_0033[2]

We also touched on Bernouilli’s principle. This is when the body forces are negligible. i.e. Phi=0.

Therefore Bernouilli’s equation becomes:

23

Where C is a constant, P is the pressure, Rho is the density and u is the speed.

Thus an increase in speed gives a decrease in pressure and vice versa.

We used this equation to go through some examples on pilot tubes within an oil refinery and looking at aircrafts to judge their speed.

I’m starting to understand Bernouilli’s equation a little more, but I feel I need to do some examples on this to help further my understanding.

Example sheet 3, question 5:

IMG_0091[1]

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