Solve Fluid Motion Problems: Blood Pressure & Oil Flow

[moonlit]

Hi,

I have two problems that I'm stuck on. Not really sure how to get the answer/what equation to use. Can someone help me?

1) The blood speed in a normal segment of a horizontal artery is 0.13 m/s. An abnormal segment of the artery is narrowed down by an arteriosclerotic plaque to 1/4 of its normal cross-sectional area. What is the difference in blood pressure between the normal and constricted segments of the artery?

2) Oil is flowing with a speed of 2.42 m/s through a pipeline with a radius of 0.132 m. How many gallons of oil (1 gal = 3.79 x 10-3 m3) flow in one day?

 

[Doc Al]

Here's what you need:

1) Use Bernoulli's equation. It relates pressure to speed in a fluid. (Look it up.) You'll also need the "continuity" equation:
$$V_1A_1 = V_2A_2$$, where V is speed and A is area.

2) If you understand what the above continuity equation means, you can use it to solve this one also.

 

[moonlit]

For the first problem, would it be possible to find the volume rate of flow first and then find how many gallons flow in one day? I guess I'm just having problems setting this one up...

 

[Doc Al]

Originally posted by moonlit
For the first problem, would it be possible to find the volume rate of flow first and then find how many gallons flow in one day? I guess I'm just having problems setting this one up...

You could certainly find it, but it won't help you solve the problem. Have you looked up Bernoulli?

 

[moonlit]

Yeah I've looked at Bernolli's equation but I'm not sure what numbers to plug in. I don't have the density or pressure for example so I'm kinda lost here... :(

 

[upsidedown]

First of all - all youe are asked for is the pressuredifference. You don't need the absolute pressures for that.

And the density of blood shouldn't be too hard to find. If you find nothing better take water density for a first guess ;)

 

[HallsofIvy]

Originally posted by moonlit
For the first problem, would it be possible to find the volume rate of flow first and then find how many gallons flow in one day? I guess I'm just having problems setting this one up...

Don't you mean for the second problem? That's the one that asked for "gallons per day".

Certainly you can.
"Oil is flowing with a speed of 2.42 m/s through a pipeline with a radius of 0.132 m."

You can calculate the (cross-section) area of the pipeline, calculate how far along the pipe a "section" of oil will flow in a second and find the volume of that cylinder. Now expand that to a full day.