Question

Chocolate milk is being mixed using milk (? = 1050 kg/m3) at 10 m/s, chocolate syrup (? = 1200 kg/m3), and a sucrose solution (? = 1100 kg/m3) at 1 m/s through 3 separate pipes (all with i.d. = 4 cm) into a mixer. After mixing, the chocolate milk exits the mixer via a fourth pipe (i.d. = 7 cm) at 8 m/s. Assuming that the fluids are incompressible, calculate (a) the velocity of the chocolate syrup required for the process to work; (b) the density of the final product.

Answer 1

Cross-section area of 4 cm pipe is A_in = 3.14 / 4 * 4² = 12.56 cm²

Cross-section area of 7 cm pipe is A_exit = 3.14 / 4 * 7² = 38.465 cm²

a)

Since fluids are incompressible, by volume conservation, we get

A_in * V_milk + A_in * V_syrup + A_in * V_sucrose = A_exit * V_chocmilk

12.56 * (10 + V_syrup + 1) = 38.465 * 8

V_syrup = 13.5 m/s

b)

By mass conservation:

(rho*A*V)_milk + (rho*A*V)_syrup + (rho*A*V)_sucrose = (rho*A*V)_chocmilk

12.56*(1050*10 + 1200*13.5 + 1100*1) = rho_chocmilk * 38.465 * 8

Density of final product rho_chocomilk = 1134.7 kg/m³

answered by: anonymous