Filter Pump Watch

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Report Thread starter 12 years ago
I have a question I was hoping someone could answer:

A filter pump is created and can be explained by the Bernoulli effect. Water is passed down the tube through nozzle N (at A), at speed v and then to B. This causes a pressure difference between A and B. This difference is measured and recorded.
Now water is replaced by a fluid with a density that is greater than water's, but the speed, v, remains constant.
State the effect this has on the pressure difference between A and B.
(I've attached a diagram, but it's not too good)
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Badges: 2
Report 12 years ago
I use p for pressure and d for density:

Bernoulli's Equation: p + 1/2dv^2 + dgh = constant along a streamline.

At A: p_1 + 1/2dv^2 + dgh_1 = constant
At B: p_2 + 1/2dv^2 + dgh_2 = constant

We can equate the two:

p_1 + 1/2dv^2 + dgh_1 = p_2 + 1/2dv^2 + dgh_2
I'm assuming velocity is constant, therefore the 1/2dv^2 term cancels

p_1 - p_2 = dgh_2 - dgh_1
p_1 - p_2 = d(gh_2 - gh_1)

Now we introduce a new liquid with a greater density, call this density d`. From the same principles as before we have:

p_1 - p_2 = d`(gh_2 - gh_1)

d` > d therefore the pressure difference has increased (h_1 and h_2 are the same in both cases)

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