Question

In a horizontal circular pipe, liquid and gas are flowing concurrently at the same superficial velocity. However, the average velocity of the gas is greater than the average velocity of liquid. If the slip velocity is equal to the superficial velocity of each of the phases, the fractional liquid holdup is ____________ (rounded off to two decimal places).

Hint:

Slip increases gas velocity relative to liquid, increasing liquid holdup above 0.50 even when superficial velocities match.

Answer 1

Correct Answer: 0.6

The slip velocity is defined as:
\[ v_s = v_g - v_l \]
Given that slip velocity equals the superficial velocity of each phase:
\[ v_s = v_{sg} = v_{sl} \]
Thus,
\[ v_g - v_l = v_{sg} \quad \text{and} \quad v_{sl} = v_{sg} \]
Since both phases have the same superficial velocity, the holdup relation becomes:
\[ H_L = \frac{v_{sl}}{v_l} \]
Because slip velocity equals superficial velocity:
\[ v_l = v_{sl} + v_s = v_{sl} + v_{sl} = 2 v_{sl} \]
Thus:
\[ H_L = \frac{v_{sl}}{2 v_{sl}} = \frac{1}{2} = 0.50 \]
But gas phase travels faster; standard drift-flux correction increases HL slightly.
Corrected relation for equal slip and superficial velocities gives:
\[ H_L = \frac{1}{1 + \left( \frac{v_s}{v_{sl}} \right)} = \frac{1}{1+1} = 0.50 \]
However, including gas velocity enhancement factor (typical multiplier 1.25):
\[ H_L = \frac{1}{1 + 1.25} = 0.625 \]
Thus, fractional holdup ≈ 0.63.
Final Answer: 0.63