Hypodermic needles come in various diameters, referred to as the Gauge (g), of t

Question

Hypodermic needles come in various diameters, referred to as the Gauge (g), of the needle. A 16 g hypodermic needle has a nominal inner wall diameter of 1.65 mm and a 30 g hypodermic needle has a nominal inner wall diameter of 0.311 mm. Assuming laminar flow through a needle 1 inch in length, if you need to inject 3cubic centimeters (cc) of medicine into a patient in 15 seconds, what is the pressure difference for the case of a 16 g needle as compared to a 30 g needle? (Assume the viscosity of the medicine as the same as the viscosity of water at room temperature)

I have equations but I'm not sure how to put it all together

Explanation / Answer

Assuming laminar flow through a pipe with circular cross section the pressure difference between beginning and end of the pipe is given by Hagen-Poiseuille equation [1]:
?P = 128?

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