1. ## Question...

A hypodermic syringe has a plunger area of 2.5 cm$\displaystyle ^2$and a 5.0 x 10$\displaystyle ^-3$ -cm$\displaystyle ^2$ needle. (a) If a 1.0 N force is applied to the plunger, what is the gauge pressure in 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 50mm Hg, what force must be applied on the plunger so that fluid can be injected into the vein?

2. Originally Posted by John 5
A hypodermic syringe has a plunger area of 2.5 cm$\displaystyle ^2$and a 5.0 x 10$\displaystyle ^-3$ -cm$\displaystyle ^2$ needle. (a) If a 1.0 N force is applied to the plunger, what is the gauge pressure in 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 50mm Hg, what force must be applied on the plunger so that fluid can be injected into the vein?
a)
$\displaystyle P = \frac{F}{A} = \frac{1.0~N}{2.5~cm^2} = \frac{1.0~N}{2.5 \times 10^{-4}~m^2} = 4000~Pa$

Now, this is absolute pressure, so we need to subtract atmospheric pressure (101 kPa or so), so the gauge pressure is $\displaystyle |101 \times 10^3 ~Pa - 4000~Pa| = 97000~Pa$

b) Does the obstruction completely block the syringe? If so then there is exactly 1 N of force. The fluid (presumably) will not compress and thus transmits forces perfectly.

c) $\displaystyle 50~mmHg = 6666.12~Pa$

So we need to exert at least this much pressure. Thus
$\displaystyle 6666.12~Pa = \frac{F}{2.5 \times 10^{-4}~m^2}$

Thus
$\displaystyle F = (6666.12~Pa)(2.5 \times 10^{-4}~m^2) = 1.66653~N$

(Edit: That's a much nicer answer! )

-Dan

3. Originally Posted by topsquark
...

c) $\displaystyle 50~mmHg = 0.37503~Pa$

...
Hello,

I don't want to pick at you but I've got:

$\displaystyle \frac{x}{101000~Pa} =\frac{5~cm}{760~cm}~\Longrightarrow~x \approx 665~Pa$

4. Originally Posted by earboth
Hello,

I don't want to pick at you but I've got:

$\displaystyle \frac{x}{101000~Pa} =\frac{5~cm}{760~cm}~\Longrightarrow~x \approx 665~Pa$
Actually, we're both wrong. 101325 Pa = 760 mm Hg, so
$\displaystyle \frac{x}{101325~Pa} = \frac{50~mmHg}{760~mmHg}$

gives $\displaystyle x = 6666.12~Pa$

I've fixed the error in the post below.

-Dan