Answer:
The average velocity of the needle exit flow is 163.27 m/s
Explanation:
Given;
inside diameter of the syringe, dā = 20 mm
inside diameter of the needle, dā = 0.7 mm
steady flow rate of the plunger, v = 20 mm/s
Apply continuity equation;
[tex]Q_{in} = Q_{out}[/tex]
Considering 0.1 of the volume flowrate out the needle opening, we will have the following equations.
[tex]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[/tex]
Therefore, the average velocity of the needle exit flow is 163.27 m/s
