If the velocity of the fluid does NOT change with respect to time, the flow is said to be a/an:
Try it first: pick an option, then read the explanation.
Asked in SSC JE 06/06/2024 (04pm-06pm)
Detailed Explanation
Fluid flow is classified based on how flow properties vary with time and space. A flow where velocity, pressure, and density at every point remain invariant over time is termed steady flow.
Steady flow condition at any fixed point:
\[ \left(\frac{\partial \mathbf{v}}{\partial t}\right)_{x,y,z} = 0, \quad \left(\frac{\partial p}{\partial t}\right)_{x,y,z} = 0, \quad \left(\frac{\partial \rho}{\partial t}\right)_{x,y,z} = 0 \]
In contrast, uniform flow requires zero spatial variation at any instant: \(\left(\frac{\partial \mathbf{v}}{\partial s}\right)_{t} = 0\).
Why “steady flow” Is Correct
By definition, steady flow requires that all flow parameters at any spatial location remain constant with time. Because the problem statement specifies no change with respect to time, the flow is steady.
Why the Other Options Are Wrong
- A. unsteady flow: Unsteady flow occurs when velocity or pressure at a given point varies with time (∂v/∂t ≠ 0).
- B. non-uniform flow: Non-uniform flow refers to velocity changing from point to point along the streamline at a given instant.
- C. uniform flow: Uniform flow refers to velocity remaining identical along the path of flow in space at any instant (∂v/∂s = 0), not invariance with time.
Key Point
∂v/∂t = 0 defines steady flow; ∂v/∂s = 0 defines uniform flow.
Key Concepts for Students
- Steady flow means conditions at any fixed point do not vary with time.
- Uniform flow means velocity does not vary from point to point along the streamline at a given instant.
- A flow can be steady and non-uniform, such as flow through a tapering pipe at constant discharge.
Practice more: this is question 3 in Properties of Fluid MCQs – Part 1. Try the whole set and check every answer instantly.