# Reaaranging a Bernoulli Equation.

1. Apr 18, 2012

### LemoneyF

1. The problem statement, all variables and given/known data

How can I rearrange this equation to graphically show that hole diametre is inversely proportional to sink time? So my experiment results show a nice diametre=1/t , and I would now like to take the equation ive come up with to show this relationship within the equation somehow. I was thinking the obvious way to do this would be to move the hole diametre on its own somehow and have time in the denominator of a fraction, im not really sure.

Its not meant to be a worked equation, just show the inverse relationship in the equation.

Changing the velocity on the sink time side into an s/t gives a time to play around with, and changing the velocity on the cup side into a flow rate/cross sectional area gives a diametre.

2. Relevant equations

diametre=1/t

P1 + 1/2pv1^2 = P2 + 1/2pv2^2

Applying equation changes-

P1 + 1/2p(s/t)^2 = P2 + 1/2p(Q / pi x 1/2 diametre^2)^2

3. The attempt at a solution

Its not correct, but was thinking something along-

P1 + 1/2p (pi x 1/2 diametre^2)^2 = P2 + 1/2p (Q / (s/t) )

2. Apr 18, 2012

### LawrenceC

If I understand the experiment, you are draining a sink of liquid and wish to show the time to drain is is inversely proportional to the diameter of the drain.

Hint: Write a differential equation that equates the outflow of liquid to the change in height of the liquid's surface in the sink. Solve it which results in the liquid level as a function of time. The differential equation would be based on the Bournoulli equation to represent the velocity at the drain. You will see how the time is affected by the diameter.