Question

A 4.5 mL syringe has an inner diameter of 6.0 mm , a needle inner diameter of 0.29 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 whose blood pressure is 140/100. Assume the liquid is an ideal fluid.

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

B. The nurse empties the syringe in 5.0 s . What is the flow speed of the medicine through the needle?

Answer 1

We know that, the blood pressure of a patient is (140/100).

The minimum fluid pressure needs to be 100 mm of Hg above atmospheric pressure.

Mathematically, we have

760 mm of Hg = 1 atm

1 atm = 1.013 x 10⁵ Pa

Then, the minimum fluid pressure will be given as -

P_fluid = 1.333 x 10⁴ Pa

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

using a formula, we have

F = P_fluid A_syringe

F = (1.333 x 10⁴ Pa) ( r_syr²)

F = [(1.333 x 10⁴ Pa) (3.14) (3 x 10^-3 m)²]

F = 0.376 N

B. The nurse empties the syringe in 5.0 s. What is the flow speed of the medicine through the needle?

using a formula, we have

v = Q / A = (V / t) / ( r_ne²)

where, V = volume of syringe = 4.5 mL = 4.5 x 10^-6 m³

t = time taken by nurse to empties the syringe = 5 s

r_ne = radius of a needle = 0.145 x 10^-3 m

then, we get

v = (4.5 x 10^-6 m³) / [(5 s) (3.14) (0.145 x 10^-3 m)²]

v = [(4.5 x 10^-6 m³) / (3.300925 x 10^-7 m².s)]

v = 13.6 m/s