A hypodermic syringe has a plunger of area 2.5cm^2 and a 5.0X10^-3cm^2 needle.?

Question

A) if a 1.0N force is applied to the plunger, what is the gauge pressure int the syringe's chamber?
B) If a small obstruction is at the end of the needle, what force does the fluid exert on it?
C) If the blood pressure in a vein is 50 mm hg, What force must be applied on the plunger so that fluid can be injected into the vein?

Answer 1

Ok, for these questions we're going to assume the fluid pressure throughout the needle is constant.

1. We're looking for the pressure exerted by the plunger on the fluid in the syringe chamber.

P = F/A is the formula we use for pressure.

P = 1N / 2.5 x 10^-2 m^2

P = 40 Pa of pressure. Final answer.

2. We can use the same formula as above and apply it to this equation. We already know the pressure exerted on the fluid and assuming it's constant through the syringe we can use the pressure we got for our previous answer to find this one.

P = F/A

We know the area of the needle opening, and the pressure of the fluid in the chamber. So we need to find F, so to do that we rearrange our equation as follows.

P * (A) = (F/A) * (A)

F = PA

F = (40 N/m^2) * (5 x 10^-5 m^2)

F = 2 x 10^-3 N Final answer.

3. In this one we know the pressure of the fluid coming out the end of the needle needs to be greater than or equal to 50 mm hg. First we need to convert mm hg to pascals which is the unit of pressure we'll be using.

We'll use dimensional analysis to convert the units.

a. 50 mm hg x 133.32 Pa / 1 mm hg = 6.666*10^3 Pa

Now we have to find the force required to equal the pressure required to inject the fluid into the vein from the plunger.

b. F = P * A

c. F = 6.666*10^3 N/m^2 * 2.5 x 10^-2 m^2

d. F = 166.65 N is required force on the plunger to create 50 mmhg of pressure on the fluid to inject it.

Answer 2

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RE:
A hypodermic syringe has a plunger of area 2.5cm^2 and a 5.0X10^-3cm^2 needle.?
A) if a 1.0N force is applied to the plunger, what is the gauge pressure int the syringe's chamber?
B) If a small obstruction is at the end of the needle, what force does the fluid exert on it?
C) If the blood pressure in a vein is 50 mm hg, What force must be applied on the plunger so that...

Answer 3

The gauge pressure is the pressure in excess of atmospheric; the needle vents to the atmosphere, so internal pressure is 1N/2.5cm^2 = 0.4 N/cm^2

F = Pi*An (internal pressure time needle area) = 0.4 N/cm^2 * 5.0*10^-3cm^2 = 0.002N

15mmHg = 15 torr = 15 torr*133.3 pa/torr=2000 pa = 2000N/m^2 = 0.2N/cm^2. For an area of 2.5 cm^2, the force is 2.5*0.2 = 0.5N