Continuity / conservation of mass

Question

Two different incompressible fluids a and b flow into a chamber through two circular ports of area 0.1 and 0.2 m² respectively.

• Fluid a is of density 1,200 kgm⁻³ and flows directly into the chamber at a speed of 2 ms⁻¹.
• Fluid b has a density of 1,500 kgm⁻³ and has a velocity normal to the surface of the chamber inlet port surface of 3 ms⁻¹.
• The chamber has a single outlet port of area 0.3 m².

What is the density and the speed of the mixture coming out of the outlet?

The answer in the back of the textbook says the correct answer is 2.6 m/s for the velocity and 1461 kg/m³ for the density. Does anyone know why my numbers are slightly off, is it possibly due to the fact that fluid B enters normal to the surface. I have attached the question below.

Thanks in advance for any help

Answer 1

The answer rounded the exit velocity to 2.6 instead of 2.67, then, again, dropped the fraction (0.54) after the decimal point:

$\gamma_c = \dfrac{(1200*0.1*2)+(1500*0.2*3)}{(0.3*2.6)} = 1461(.54)$