Question

1. The unsteady flow of glycerin is such that at A it has a velocity of VA = (5t1/2) m/s, where t is in seconds. Determine the acceleration of a fluid particle located at x = 0.3 m when t = 1 s. Hint Determine V = V(x,t), then find the material derivative.

2. The cylindrical plunger traveling at VP = (0.004t1/2) m/s, where t is in seconds, injects a liquid plastic into the mold to make a solid ball. If d = 50 min, determine the amount of time needed to do this. The volume of the ball is V = 4/3(pi)(r3).

3..The cylinder is pushed down into the tube at a rate of V = 5 m/s. Determine the velocity of the liquid as it rises in the tube.

Answer 1

$$a(t)=\frac{5}{2\sqrt{t}}\\a(1)=\frac{5}{2\sqrt{1}}=2.5\frac{m}{s^2}$$