Question

The type of flow, if \(\dfrac{\partial v}{\partial s}=0\), is

• A. Uniform flow
• B. Non-uniform flow
• C. Steady flow
• D. Unsteady flow

Hint:

Flow classifications: \[ \boxed{ \begin{aligned} \frac{\partial v}{\partial s}=0 &\Rightarrow \text{Uniform Flow}\\[2mm] \frac{\partial v}{\partial t}=0 &\Rightarrow \text{Steady Flow} \end{aligned} } \]

Answer 1

The Correct Option is A

Step 1: Two separate ways flow can vary.
Flow behaviour is checked against two different variables. Change with time, $\partial v/\partial t$, tells us whether flow is steady or unsteady. Change with position along the flow path, $\partial v/\partial s$, tells us whether flow is uniform or non-uniform.
Step 2: Reading the given condition.
Here we are told $\partial v/\partial s = 0$, which is the position based derivative, not the time based one.
Step 3: Naming the flow type.
A velocity that does not change from one point to the next along the flow direction, at a given instant, is by definition uniform flow, regardless of what is happening with time.
\[ \boxed{\text{Uniform flow}} \]