Ahypodermic syringe (see fig. p5.30) is used to apply a vaccine. if the plunger is moved forward at the steady rate of 20 mm/s and if vaccine leaks past the plunger at 0.1 of the volume flowrate out the needle opening, calculate the average velocity of the needle exit flow. the inside diameters of the syringe and the needle are 20 mm and 0.7 mm.

There is a sweet potato with an initial uniform temperature of 25 c and it has an average diameter of 70 mm. thermal conductivity and diffusivity of the potato are 0.62 w/m c and 0.2 x 10^-6 m^2/s. respectively. it is to be cooled by refrigerated air at 1.8°c flowing at a velocity of 4 m/s. the average heat transfer coefficient between the potato and the air is 25 w/m2·°c. determine how long it will take for the center temperature of the potato to drop to 5.5°c