Question

The flow of incompressible fluids without the presence of shear is referred to as

• A. Potential flow
• B. Turbulent flow
• C. Laminar flow
• D. Fully developed flow

Hint:

Potential flow describes an inviscid, irrotational, and often incompressible flow where shear stresses are absent due to the lack of viscosity.

Answer 1

The Correct Option is A

Step 1: Understand the characteristics of the flow. 
The problem describes the flow of an incompressible fluid without the presence of shear. In fluid dynamics:
Shear refers to the viscous forces that cause layers of fluid to slide past each other, resulting in velocity gradients. Shear is associated with viscosity and is present in flows where friction plays a role.
Incompressible fluid means the density is constant (\( \nabla \cdot \mathbf{v} = 0 \), where \( \mathbf{v} \) is the velocity field). 
Step 2: Identify the type of flow without shear. 
Potential flow: This is an idealized flow where the fluid is inviscid (no viscosity), irrotational (\( \nabla \times \mathbf{v} = 0 \)), and incompressible. Since there is no viscosity, there are no shear stresses (\( \tau = \mu \frac{\partial u}{\partial y} = 0 \) when \( \mu = 0 \)). Potential flow is described by a velocity potential \( \phi \), where \( \mathbf{v} = \nabla \phi \), and it satisfies Laplace’s equation \( \nabla^2 \phi = 0 \).
Turbulent flow: This involves chaotic motion with eddies and mixing, where shear is present due to viscosity and velocity gradients.
Laminar flow: This is a smooth, orderly flow where layers slide past each other, but shear is present due to viscosity (e.g., in a pipe, \( \tau = \mu \frac{\partial u}{\partial r} \)).
Fully developed flow: This refers to a flow (e.g., in a pipe) where the velocity profile no longer changes along the flow direction, but shear is still present due to viscosity.
Since the flow has no shear, it must be inviscid, which aligns with potential flow. 
Step 3: Evaluate the options. 
(1) Potential flow: Correct, as potential flow assumes an inviscid fluid, meaning no shear stresses, and is consistent with an incompressible fluid without shear. Correct.
(2) Turbulent flow: Incorrect, as turbulent flow involves shear due to viscosity and velocity fluctuations. Incorrect.
(3) Laminar flow: Incorrect, as laminar flow involves shear due to viscosity, even though the flow is orderly. Incorrect.
(4) Fully developed flow: Incorrect, as fully developed flow (e.g., in a pipe) involves shear due to viscosity, even if the velocity profile is constant along the pipe. Incorrect. 
Step 4: Select the correct answer. 
The flow of incompressible fluids without the presence of shear is referred to as potential flow, matching option (1).