Calculating Force Needed to Push Fluid into a Vein at 18 mm Hg Pressure

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To calculate the force needed to push fluid into a vein at 18 mm Hg pressure, the density of mercury is essential, which is approximately 1.3534e-4 kg/m³ after conversion. The gauge pressure of 18 mm Hg translates to about 133 N/m². The equation F1 = P1/A1 is used, where pressure is derived from the density of mercury multiplied by gravitational acceleration and the area of the plunger. The user is struggling with determining the correct diameter for the plunger in their calculations. Clarification on conversions and the appropriate diameter is needed to resolve the issue.
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What force on the plunger would be needed to push fluid into a vein where the gauge pressure is 18 mm Hg? Answer for the instant just before the fluid starts to move.

I know i need the density of mercury (in Meters) and that equals = 13.534e-3 / 100 which is

1.3534e-4 for the density

Next i did the conversion of the atm pressure of mercury and got 133 n / m2. (i think that's correct)

ok so i know i need to use pascals and i developed my equations i was given and ended with

F1 = P1/ A1

Which is

Density mercury * atm pressure mercury * 9.8 / pie * D^2

I think that is the correct equation and when i use it i get the wrong answer.

What I am really stuck with is what i use as the diameter.

Any help would be great if i messed up any conversions and what not. TY
 
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