- Joined
- May 10, 2010
- Messages
- 78
- Reaction score
- 1
I'd love an explanation for problem 7.5b in the Fluids/Solids review in Berkeley review.
The question:
Which single change makes it easiest (ie: creates the smallest pressure difference between your mouth and the atmosphere) to drink a milkshake.
A) Increase the straw length by 50% but keeping the flow rate and milkshake fixed.
B) Decreasing the straw radius by 50%, but keeping the flow rate and milkshake fixed.
C) Melting the shake until viscosity drops by 50%, but keeping the flow rate and straw fixed.
D) Drinking the shake at 25% of the usual flow rate, without changing the straw or shake.
It's one of the questions that doesn't offer an explanation, but gives the correct answer as D.
My thought process is to use the Poiseulle's principle equation for flow rate Q:
Q = [(pi*r^4)/(8nL)]*(P1-P2)
and treat is as Q=A*B for a relationship.
where n=coefficient of viscosity, L=length of straw
So we want the pressure difference P1-P2 to be smallest (ie: B smallest). I eliminated answers A and B because if Q is fixed, both decreasing r and increasing L results in an overall lower value for the A part of the equation which would increase the pressure difference B.
I answered C, because decreasing viscocity, or n in the equation, would result in a higher value for the A part of the equation and thus a lower B, or pressure difference, if Q is fixed.
D, the correct answer, results in a Q increase 25% without changing the straw radius, length, or viscosity.
So by Q=A*B again, increasing Q and keeping A constant would increase B, the pressure difference....right? And we want the smallest pressure difference so I don't see how that is right.
I hope my wording wasn't too confusing. If anyone can correct me or offer an explanation I would be much appreciative!
The question:
Which single change makes it easiest (ie: creates the smallest pressure difference between your mouth and the atmosphere) to drink a milkshake.
A) Increase the straw length by 50% but keeping the flow rate and milkshake fixed.
B) Decreasing the straw radius by 50%, but keeping the flow rate and milkshake fixed.
C) Melting the shake until viscosity drops by 50%, but keeping the flow rate and straw fixed.
D) Drinking the shake at 25% of the usual flow rate, without changing the straw or shake.
It's one of the questions that doesn't offer an explanation, but gives the correct answer as D.
My thought process is to use the Poiseulle's principle equation for flow rate Q:
Q = [(pi*r^4)/(8nL)]*(P1-P2)
and treat is as Q=A*B for a relationship.
where n=coefficient of viscosity, L=length of straw
So we want the pressure difference P1-P2 to be smallest (ie: B smallest). I eliminated answers A and B because if Q is fixed, both decreasing r and increasing L results in an overall lower value for the A part of the equation which would increase the pressure difference B.
I answered C, because decreasing viscocity, or n in the equation, would result in a higher value for the A part of the equation and thus a lower B, or pressure difference, if Q is fixed.
D, the correct answer, results in a Q increase 25% without changing the straw radius, length, or viscosity.
So by Q=A*B again, increasing Q and keeping A constant would increase B, the pressure difference....right? And we want the smallest pressure difference so I don't see how that is right.
I hope my wording wasn't too confusing. If anyone can correct me or offer an explanation I would be much appreciative!
