A 3.5 mL syringe has an inner diameter of 6.0 mm , a needle inner diameter of 0.

Question

A 3.5 mL syringe has an inner diameter of 6.0 mm , a needle inner diameter of 0.24 mm , and a plunger pad diameter (where you place your finger) of 1.2 cm. A nurse uses the syringe to inject medicine into a patient's vein and so has to push against the patient's blood pressure which is 140 over 100. Assume the liquid is an ideal fluid and so the pressure in the medicine is the same as the pateint.

A. What is the minimum force the nurse needs to apply to the syringe?

B.The nurse empties the syringe in 4.3 s . What is the flow speed of the medicine through the needle and into the vein?

Explanation / Answer

A)

blood pressure

p = 140mmHg * 1.01e5Pa / 760mmHg = 18665 Pa

force against end of syringe

F = p*A = 18665Pa * (0.00600m)²/4 = 0.528 N

B)

Q = V / t = 3.50mL / 4.30s = 0.814 mL/s = 0.814 cm³/s

Then velocity

v = Q / A = 0.814cm³/s / ((0.0240cm)²/4) = 1799.23 cm/s

or 17.99 m/s (nearly 18 m/s)

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