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).

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

what is the question because that is not a question.

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