Question

According to the conservation law, “Net mass flow across the fluid element is equal to the rate of change of mass inside the element”. But, stating the final equation, “Net mass flow across the fluid element + the rate of change of mass inside the element = 0”. Why is the operation not subtraction?

(a) Irrespective of the law, the sum is always zero

(b) The two terms are always opposite in sign

(c) Change in sign is not considered

(d) Rate of change may be increase or decrease

The question was posed to me in unit test.

The question is from Continuity Equation in section Governing Equations of Fluid Dynamics of Computational Fluid Dynamics

Answer 1

The correct option is (b) The two terms are always opposite in sign

The explanation: The “net mass flow across the fluid element” being positive means that it is outward flow. If flow is outward, mass inside the fluid element decreases leading to a negative “rate of change of mass inside the element”. Thus, the two terms are always opposite in sign that they can be summed up to get zero.