Question

A hypodermic syringe contains a medicine with the density of water (figure below). The barrel of the syringe has a cross-sectional area of 2.92 ✕ 10−5 m2. In the absence of a force on the plunger, the pressure everywhere is 1.00 atm. A force F of magnitude 1.80 N is exerted on the plunger, making medicine squirt from the needle. Determine the medicine's flow speed through the needle. Assume the pressure in the needle remains equal to 1.00 atm and that the syringe is horizontal.

Answer 1

The pressure inside the syringe is
P= Force/area of syringe = F/A = 1.80 / (2.92 ✕ 10⁻⁵) = 61644 Pa

It is also the pressure difference between syringe and needle

By Bernoulli's principle,

v is the fluid flow speed at a point on a streamline,

g is the acceleration due to gravity,

z is the elevation of the point above a reference plane

p is the pressure at the chosen point

ρ is the density of the fluid at all points in the fluid.(for water it is 1000 kg/m³ )

and since the syringe is horizontal, z = 0 and velocity at leftmost cross section of syringe = 0

let exist velocity from needle = v

Hence from above equation
ΔP= ½ρv²

61644= ½ x 1000 x v²
v = 11.10 m/s

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