Fluids & Solids Questions

[HopefulOncoDoc]

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Hey guys I have some questions on the Fluids and Solids portion of Physics.

1) Given that the density of seawater is 1.05 g/mL and the density of oil is 0.90 g/mL, at what depth in a tank of oil is the gauge pressure the same as it is at 12m below the surface in a tank of seawater?

A. A depth of 10.0 m in oil
B. A depth of 10.4 m in oil
C. A depth of 13.6 m in oil
D. A depth of 14.0 m in oil

The answer is D.

2) Releasing adrenaline dilates blood vessels, making it easier for blood to flow. By about what percentage would the diameter of a blood vessel need to increase to raise blood flow by 20%, at constant blood pressure?

A. 0%
B. 4.7%
C. 10%
D. 20%

The answer is B.

3) Suppose a mass M is suspended by a wire of length L, and radius R stretches a wire by ΔL. By how much will a wire that is twice as long and twice the diameter stretch when the same mass, M, is suspended by it?

A. 4ΔL
B. 2ΔL
C. ΔL/4
D. ΔL/2

I tried to solve this question using Young's Modulus (Stress/Strain);

ΔL = FL/E(πr^2) -> ΔL = F(2L)/E(π(2)^2) -> ΔL = F(2L)/E(4&#960😉

ΔL = FL/E(2&#960😉 = 2ΔL ??

But the answer is D? What did I do wrong?

Thanks a lot everyone.

 

[GoodmanBrown]

Hey, Onc. So here's what I've got.

1) Use the static part of Bernoulli's here. Pressure = density x gravity x depth.
Gravity is the same and can be ignored. We know pressure is the same for both sides. The equation comes out to: p1 = p2 -> density1 x depth1 = density2 x depth2. -> 1.05 x 12m = 0.90 x oil depth. Easy. oil depth = 1.05 x 12 / 0.90 = 14m.

2) This one is trickier and I wouldn't have got it on my MCAT (but it wasn't asked...). Use the Hagen-Poiseuille equation. It's on wikipedia under Blood Flow. Basically it says that resistance is associated with radius ^4. So, since they're the only two pieces that change in the problem, you just find the 4th root of 1.20. (1.20)^(1/4) = 1.047 leads you to your answer. This is probably the hardest conceptually to understand.

3) This is tricky. You have all the parts right and just barely missed the finish line. You need to differentiate delta L 1 vs. delta L 2.
Delta L 1 = FL/EA. You're right there. (That's what the problem gives you.)
Delta L 2 = FL*2/(EA*4) which is what you have.
But delta L 2 = (FL/EA) / 2 which you have also. But, if you look, (FL/EA) = delta L 1.
So, our goal, delta L 2 = delta L 1 / 2. So, that's why the answer is D and not B. You need to always remember you actually have two different delta L's you're finding. Your equation delta L = 2*delta L can never be true unless delta L = 0 which makes no sense here. Be sure to keep track of subscripts. You're using the same equation, but in two different circumstances, so the quanitities will be different.

Hope that helps.

 

[inaccensa]

Hey, Onc. So here's what I've got.

1) Use the static part of Bernoulli's here. Pressure = density x gravity x depth.
Gravity is the same and can be ignored. We know pressure is the same for both sides. The equation comes out to: p1 = p2 -> density1 x depth1 = density2 x depth2. -> 1.05 x 12m = 0.90 x oil depth. Easy. oil depth = 1.05 x 12 / 0.90 = 14m.

2) This one is trickier and I wouldn't have got it on my MCAT (but it wasn't asked...). Use the Hagen-Poiseuille equation. It's on wikipedia under Blood Flow. Basically it says that resistance is associated with radius ^4. So, since they're the only two pieces that change in the problem, you just find the 4th root of 1.20. (1.20)^(1/4) = 1.047 leads you to your answer. This is probably the hardest conceptually to understand.

3) This is tricky. You have all the parts right and just barely missed the finish line. You need to differentiate delta L 1 vs. delta L 2.
Delta L 1 = FL/EA. You're right there. (That's what the problem gives you.)
Delta L 2 = FL*2/(EA*4) which is what you have.
But delta L 2 = (FL/EA) / 2 which you have also. But, if you look, (FL/EA) = delta L 1.
So, our goal, delta L 2 = delta L 1 / 2. So, that's why the answer is D and not B. You need to always remember you actually have two different delta L's you're finding. Your equation delta L = 2*delta L can never be true unless delta L = 0 which makes no sense here. Be sure to keep track of subscripts. You're using the same equation, but in two different circumstances, so the quanitities will be different.

Hope that helps.

The 2nd q doesnot make sense. Do you think there is another way to solve it.

 

[GoodmanBrown]

The 2nd q doesnot make sense. Do you think there is another way to solve it?

Not sure. At its simplest, blood flow = pressure / resistance.

Resistance can be approximated by the Hagen-Poiseuille equation which I mentioned. That's:

resistance = viscosity of fluid x length x 8 / (radius^4 x pi). So, that's where I got my answer. I'm a bit confused as to why it's not just r^2 myself, but I've reached the limits of my knowledge there.