Question

A vaccination gun can force its contents through a small aperture a few thousanths of an inch in diameter at high pressures ( 550 psi) and so avoids using a hypodermic syringe and sticking the patient. Using Bernoulli's equation, how fast does the fluid leave such a gun? Take the density of the vaccine as 1100 kg/m^3 and assume the flow speed in the reservoir within the gun can be neglected. In contrast, using the equation of continuity, estimate how fast fluid leaves an insulin syringe, which has an inner diameter of 0.11 mm. The body is about 0.5 cm in diameter. You may assume the plunger goes in at 3 cm/s.

Answer 1

2. Given: R 550psi 3.792x10s Pa B = 1.01x105 Pa Density (ρ)-1 100 kg/m Let the required speed will be v . From Bemoulli's equati on we have, 2x(3.792x106-1.01x10 1100 v=81.92 m/s Therefore, the required speed is v-81.92m/s Now from continuity equation we have, ух(rx(0.11x10-3)2)-π×(0.5 x 10-2)2 x 3 x 10-2 π×(0.5×10-2)2×3×10-2 π×(0.11×10-3 % -61.98 m/s Therefore, the speed fluid is | y = 6198 m/s