Question

Two gaseous streams enter a combining tube and leave as a single mixture. These data apply at the entrance section:

For one gas : A₁ = 55 cm² U₁ = 400fps    v1 = 10 ft³/lb_m

For another gas: A₂ = 50 cm²  m₂ = 12.22lb_m/s    р = 00.12lb_m/ft³

At exit section: U₃ = 350 fps      v₃ = 8ft³/lb_m

Find (a) U₂ at section 2 (b) mass flow rate at the exit

Answer 1

$A_1 = 55 \;cm^2 = 0.0592 \;ft^2 \\ U_1 = 400 \;fps \\ v_1 = 10 \;ft^3/lb \\ P_1 = 0.1 \;\frac{lb}{ft^3} \\ A_2 = 50 \;cm^2 = 0.0538 \;ft^2 \\ m_2 = 12.22 lb/s \\ P_2 = 0.12 \;lb/ft^3 \\ U_3 = 350 \;fps \\ v_3 = 8 \;ft^3/lb \\ P_3 = \frac{1}{8} \; lb/ft^3$

(a) To find speed at section 2

Mass flow rate at section 2:

$m_2 = P_2A_2U_2 \\ U_2 = \frac{m_2}{P_2A_2} \\ = \frac{12.22 \;lb/ft^3}{0.12 \; lg/ft^3 \times 0.0538 \;ft^2} \\ = 1892.21 \;fps$

(b) To find mass flow rate at the exit

$m_1=P_1A_1U_1 \\ m_1 = 0.1 \times 0.0592 \times 400 = 2.368 \; lb/s$

Conservation of mass

$m_3 = m_1+m_2 \\ = 2.368 + 12.22 \\ = 14.588 \;lb/s$