Question

One dimensional flow is :

• A. Steady uniform flow
• B. Uniform flow
• C. Flow which neglects changes in a transverse direction
• D. Restricted to flow in a straight line

Hint:

Dimensionality in fluid mechanics refers to how many coordinate axes are needed to track velocity changes:
- 1D Flow: Velocity varies only along the flow path (\(x\)-axis). Transverse changes (\(y\) and \(z\) directions) are neglected.
- Curved flow can still be 1D if we track it along a single curved streamline coordinate \(s\).

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Fluid flow is classified as one-, two-, or three-dimensional depending on the number of space coordinates required to describe the flow field.
In reality, all physical flows are three-dimensional, but engineers use simplifications to make calculations manageable.

Step 2: Detailed Explanation:
Let us analyze the definition of one-dimensional (1D) flow:
- In a one-dimensional flow, the fluid parameters (such as velocity, acceleration, pressure, and density) are functions of time and only one space coordinate (usually along the longitudinal axis of the conduit or centerline of flow).
- Any variations in velocity or pressure in the transverse directions (perpendicular to the main flow path) are assumed to be negligible or are averaged out.
- For example, flow through a pipe is treated as one-dimensional because we assume the velocity is uniform across any cross-section, even though friction causes it to vary from zero at the wall to a maximum at the center. We use the average velocity \(V = Q/A\), neglecting transverse variations.
Let us evaluate the options:
- Steady uniform flow (A) and Uniform flow (B) describe temporal and spatial constancy, not the spatial dimensionality.
- Restricted to flow in a straight line (D) is incorrect. A one-dimensional flow can occur along a curved path (like a curved pipe) as long as the parameters only vary along that single curved streamline coordinate \(s\).
Therefore, one-dimensional flow is a flow that neglects changes in a transverse direction.

Step 3: Final Answer:
The correct option is (C).