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  1. #1
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    Question...

    A hypodermic syringe has a plunger area of 2.5 cm ^2and a 5.0 x 10 ^-3 -cm ^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?
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by John 5 View Post
    A hypodermic syringe has a plunger area of 2.5 cm ^2and a 5.0 x 10 ^-3 -cm ^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)
    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 |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) 50~mmHg = 6666.12~Pa

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

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

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

    -Dan
    Last edited by topsquark; August 23rd 2007 at 04:49 AM.
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  3. #3
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    Quote Originally Posted by topsquark View Post
    ...

    c) 50~mmHg = 0.37503~Pa

    ...
    Hello,

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

    \frac{x}{101000~Pa} =\frac{5~cm}{760~cm}~\Longrightarrow~x \approx 665~Pa
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  4. #4
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by earboth View Post
    Hello,

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

    \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
    \frac{x}{101325~Pa} = \frac{50~mmHg}{760~mmHg}

    gives x = 6666.12~Pa

    I've fixed the error in the post below.

    -Dan
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