Solving Two Pressure Problems: IV Feeding and Hydraulic Lift"

[mikefitz]

1. The drawing shows an intravenous feeding. With the distance d=0.38 m, nutrient solution (rho = 1012 kg/m3) can just barely enter the blood in the vein. What is the gauge pressure of the venous blood? Express your answer in millimeters of mercury.

d=.38m
p=1012

P=pgh
P=1012*9.81*.38= 3 772.5336 mm ??

Now, I know this is not correct, do I need to add the atmospheric pressure to the final answer (1.01 × 105 Pa) ?

2. A hydraulic lift is lifting a car that weighs 12 kN. The area of the piston supporting the car is A, the area of the other piston is a, and the ratio A/a is 105.6. How far must the small piston be pushed down to raise the car a distance of 2 cm? [Hint: Consider the work to be done.]

I know :
d=.2m
F=1200N
A=105.6
a=1

A is pushing the car up and I need to find out how far a needs to travel in order to achieve 2m. What are the pressure formula relating distance that I could use to solve this one? Thanks!

 

[OlderDan]

1. The drawing shows an intravenous feeding. With the distance d=0.38 m, nutrient solution (rho = 1012 kg/m3) can just barely enter the blood in the vein. What is the gauge pressure of the venous blood? Express your answer in millimeters of mercury.

d=.38m
p=1012

P=pgh
P=1012*9.81*.38= 3 772.5336 mm ??

Now, I know this is not correct, do I need to add the atmospheric pressure to the final answer (1.01 × 105 Pa) ?

2. A hydraulic lift is lifting a car that weighs 12 kN. The area of the piston supporting the car is A, the area of the other piston is a, and the ratio A/a is 105.6. How far must the small piston be pushed down to raise the car a distance of 2 cm? [Hint: Consider the work to be done.]

I know :
d=.2m
F=1200N
A=105.6
a=1

A is pushing the car up and I need to find out how far a needs to travel in order to achieve 2m. What are the pressure formula relating distance that I could use to solve this one? Thanks!

mm of mercury is a way of expressing pressure. For a given pressure you need to find the height of a coulumn of mercury that would create that much pressure. You already know how to find the pressure from a height of liquid. You need to find the density of mercury and calculate the height of mercury that will give that much pressure. Guage pressure is the difference between the pressure you are measuring and atmospheric. I don't think you need to be concerned with atmospheric pressure in ths problem.

The hint for your second problem assumes you know the relationship between the forces in the hydraulic system. This is actually working backwards because the reason you know the force relationship is because you know the fluid is incompressible and has uniform pressure throughout. All you really need to know is that the volume of liquid you push out of the small cylinder goes into the big cylinder.

Check your numbers. 2cm is not .2m.

 

[mikefitz]

OlderDan,

Again, I have done the following for #1:

P=pgh
P= (1012)(.38)(9.81) = 3772.5336 Pa

p(mercury)=13570 kg/m3

How do I relate the density of mercury to the gauge presssure from the blood?

 

[OlderDan]

OlderDan,

Again, I have done the following for #1:

P=pgh
P= (1012)(.38)(9.81) = 3772.5336 Pa

p(mercury)=13570 kg/m3

How do I relate the density of mercury to the gauge presssure from the blood?

You have calculated the gauge pressure of the fluid at the vein. To express that in mm of mercury, you need to find the height of a column of mercury that would provide the same amount of pressure. Look up the density of mercury. Set ρgh equal to the pressure you calculated above and solve for the h of mercury. Convert your answer to mm, and you should have it.

In the end, the ratio of the heights of the liquids (nutrient and mercury) should be the inverse of the ratio of their densities.