Question

A hypodermic syringe is used to apply a vaccine. If the plunger is moved forward at the steady rate of 20 mm/s and if vaccine leaks past the plunger at 0.1 of the volume flowrate out the needle opening, calculate the average velocity of the needle exit flow. The inside diameters of the syringe and the needle are 20 mm and 0.7 mm.

Answer 1

Answer:

The average velocity of the needle exit flow is 163.27 m/s

Explanation:

Given;

inside diameter of the syringe, d₁ = 20 mm

inside diameter of the needle, d₂ = 0.7 mm

steady flow rate of the plunger, v = 20 mm/s

Apply continuity equation;

$Q_{in} = Q_{out}$

Considering 0.1 of the volume flowrate out the needle opening, we will have the following equations.

$0.1 *Q_{out \ of \ needle} = Q_{in\ syringe}\\\\0.1(A_2v_2) = A_1v_1\\\\v_2 = \frac{A_1v_1}{0.1A_2}\\\\ v_2 = (\frac{A_1}{A_2} )(\frac{v_1}{0.1})\\\\ v_2 = (\frac{d_1^2}{d_2^2} )(\frac{v_1}{0.1})\\\\ v_2 = (\frac{d_1}{d_2} )^2(\frac{v_1}{0.1})\\\\v_2 = (\frac{20}{0.7} )^2(\frac{20*10^{-3}}{0.1})\\\\v_2 = 163.27 \ m/s$

Therefore, the average velocity of the needle exit flow is 163.27 m/s