Question

A syringe has a fine needle with an inside diameter of 109μm. The barrel has a diameter of 2.22cm and is filled with water. Calculate the velocity of water as it squirts horizontally from the needle if you apply a force of 3.24N onto the plunger. (Hint: you may approximate the area of the barrel to be much larger than the area of the needle).

Answer 1

Answer: the velocity of water as it squirts horizontally from the needle is 4.09196 m/s

Explanation:

Given that;

inside diameter = 109μm

barrel diameter = 2.22 cm so r = 1.11 cm = 0.0111 m

force fair = 3.24 N

We know that the inside diameter is neglected; from the Bernoulli's equation

so

P_inside + 1/2pv²_inside + egy_inside = P_outside + 12pv²_outside + egy_outside

p_inside - p_outside = 1/2e_airv²outside = Fair / Abannel

Fair = 1/2painv²outside . Abannel

therefore

3.24 = 1/2(1000) v²outside (πr²)

3.24 = 1/2(1000) v²outside (π × (0.0111)²

3.24 = 0.1935 v²_outlet

v²_outlet = 3.24 / 0.1934

v²_outlet  = 16.7441

v_outlet = √16.7441

v_outlet  = 4.09196 m/s

Therefore the velocity of water as it squirts horizontally from the needle is 4.09196 m/s