Question

A 5.0 mL syringe has an inner diameter of 5.5 mm , a needle inner diameter of 0.22 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.

Part A

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

Part B

The nurse empties the syringe in 4.9 s . What is the flow speed of the medicine through the needle?

Answer 1

Minimum Pressure P = 100 mm of Hg

                               = 100 x 133.322 Pa

                                = 13332.2 Pa

Diameter d = 5.5 mm= 5.5 x10 ^-3 m

Area of crosssection A = (pi)d ² / 4

                                  = 2.375 x10 ^-5 m ²

Therefore the minimum force the nurse needs to apply to the syringe F = PA

     F = (13332.2 Pa)(2.375 x10 ^-5 m ²)

        = 0.316 N

(B).Flow rate Q = 5 mL / 4.9 s

                       = 5 x10 ^-3 L / 4.9 s

                      = 5 x10 ^-3 x 10 ^-3 m ³ / 4.9 s

                       = 1.02 x10 ^-6 m ³ / s

Area of crosssection of needle A ' = (pi)d ' ² / 4

Where d ' = diameter of the needle= 0.22 mm = 0.22 x10 ^-3 m

Therefore A ' = 3.8 x10 ^-8 m ²

So, the flow speed of the medicine through the needle v = Q /A '

         v = (1.02 x10 ^-6 m ³ / s)/(3.8 x10 ^-8 m ²)

           = 26.83 m/s