Blood pressure and needle insertion

[nfullernyg]

OK, so I'm new here and really lost on how to these two problems involving blood pressure and syringe force etc. Any help would be appreciated, and if you could somewhat explain how you solved it that would be great, so I can know how to do this in the future.

Homework Statement

1. Someone you know is in the hospital and requires the intravenous feeding of nutrients. The blood pressure in the vein of the person is 20 mmHg. This means that the pressure in the vein is 20 mmHg greater than atmospheric pressure. What is the minimum height above the insertion point for the needle into the vein that the nurse must hang the nutrient supply bottle to ensure that the nutrients flow into the patient? Assume that the fluid nutrients have the density of water. (Remember that here Hg stands for the chemical symbol of mercury and is not height times gravitational acceleration.)


2. Suppose a horse has been tranquilized to treat an illness, and an injection is necessary. Also suppose that to give the shot in a time of 2 seconds, there is required a pressure in the body of the syringe of 250 mmHg. If the plunger inside the syringe has an area of 2 cm2, how much force must the veterinarian apply to the end of the plunger to produce this pressure? (Friction with the walls of the syringe is generally quite small and can be ignored.)

Homework Equations

The Attempt at a Solution

I have no attempts because I cannot figure out where to start. I've read that mercury is 13.6 times as dense as water, but I'm not sure if that is even relevant. I tried these for a while last night, and just couldn't figure out where to even begin. Thanks for any help!

 

[nfullernyg]

ps, huge kudos if you can figure it out before i have class in 30 minutes

 

[ogb p]

Dear student,

Thank you for reaching out for help with these problems involving blood pressure and needle insertion. I am happy to assist you in understanding these concepts and solving the problems.

For the first problem, we can use the equation P = ρgh to determine the minimum height above the insertion point for the needle. Here, P represents pressure, ρ represents the density of the fluid (in this case, water), g represents the gravitational acceleration (9.8 m/s^2), and h represents the height. We can rearrange this equation to solve for h: h = P/(ρg).

In this case, P = 20 mmHg, ρ = 1000 kg/m^3 (density of water), and g = 9.8 m/s^2. Converting mmHg to mH2O (height of water), we get 20 mmHg = 20/13.6 mH2O = 1.47 mH2O. Plugging these values into the equation, we get h = 1.47/(1000*9.8) = 0.00015 meters. This means that the minimum height above the insertion point for the needle should be 0.15 millimeters to ensure that the nutrients flow into the patient.

For the second problem, we can use the equation P = F/A to determine the force required to produce a pressure of 250 mmHg. Here, P represents pressure, F represents force, and A represents the area of the plunger. We can rearrange this equation to solve for F: F = PA.

In this case, P = 250 mmHg, which is equivalent to 250/13.6 mH2O = 18.38 mH2O. Converting this to Pa (Pascals), we get 18.38*9.8*1000 = 180,024 Pa. The area of the plunger is given as 2 cm^2, which is equivalent to 0.0002 m^2. Plugging these values into the equation, we get F = 180,024*0.0002 = 36.005 Newtons. This is the amount of force that the veterinarian must apply to the end of the plunger to produce a pressure of 250 mmHg in the syringe.

I hope this explanation helps