A veterinarian uses a hypodermic syringe like the one shown in the figure to inj

Question

A veterinarian uses a hypodermic syringe like the one shown in the figure to inject a horse with a medical solution with a density that is the same as water. The barrel of the syringe has a cross-sectional area of

A veterinarian uses a hypodermic syringe like the one shown in the figure to inject a horse with a medical solution with a density that is the same as water. The barrel of the syringe has a cross-sectional area of 2.33 x10-5 m2 and before she exerts any force on the plunger, the pressure everywhere in the syringe is 1.00 atm. When she exerts a force with a magnitude of 3.05 N on the plunger, the medical solution squirts horizontally from the needle. Determine the speed of the solution as it leaves the needle.

Explanation / Answer

Note that by Bernoulli's principle,

p1 = 1/2 D v^2

As there are no potential energies involved here.

Thus, solving for v,

v = sqrt [2 p1 / (rho)]

As p1 = F/A,

v = sqrt [ [2 F] / [A D] ]

Plugging in the given values, and D = 1000 kg/m^3 for water,

v = 16.2 m/s [ANSWER]

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