# Laminar Flow

By Deepanshu Rastogi|Updated : November 24th, 2021

This article contains basic notes on the "Laminar Flow"  topic of the "Fluid Mechanics & Hydraulics" subject.

## Laminar Flow

### Laminar Flow

• Laminar flow is also known as viscous flow
• In laminar flow, viscous force is highly is highly predominant.

Case–I

#### The laminar flow between 2- parallel plates

Consider a fluid element in the flow field. An element has thickness dy, length dx and y distance from the bottom plate. Assumption:- width of flow perpendicular to paper = unity

Free body diagram of an element Apply equilibrium condition But we know that So,  are independent form y

By integrating equation (1) ⇒ Again integrate with respect to y Apply boundary condition 1. At y = 0, u = 0
C2 = 0
2. At y=H, u=0 So,  Maximum velocity Mean velocity

Mass flow rate = Mass flow rate, when considering average velocity. By equating both terms {from eq. (a) and (b)} and putting the expression of  From expression of  #### Shear stress distribution:

By Newton’s Law of viscosity  #### Pressure difference b/w two points along the flow

Consider average velocity expression  Laminar flow through pipe: (circular) Consider a fluid element having radius r and length dx

Free body diagram of an element Apply horizontal equilibrium equation

Internal flow:- According to Newton’s Law of Viscosity from first figure in this section put the value of in eq. (a) By integrating it At ---no slip condition #### Maximum Velocity: So from the expression of u, put r=0 #### Mean Velocity:

Mass flow rate is constant throughout the pipe From the expression of  Pressure distribution:

In the calculation of pressure difference always consider average velocity So. By Rearranging  #### Velocity and shear stress profile in a circular pipe • Flow between Flat plate
We know that  • Circular pipe flow
We know that Head Loss  NOTE:

• Dependency of flow on Reynolds number
Reynolds number  density of fluid Velocity of flow Dynamic Viscosity Characteristic dimension
For Laminar flow If, Turbulent flow
• If, 2000 transition flow

• Head Loss equation by Darcy’s Here Friction factor Velocity (average) Length of pipe Diameter of pipe
This equation is valid for both turbulent and laminar flow.
• Friction factor for circular pipe flow
In circular pipe But Darey’s equation By equating both expressions If you are preparing for ESE/ GATE or other PSU Exams (Civil Engineering), then avail Online Classroom Program for ESE and GATE CE:

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