Pipe Flow

Introduction:

Pipes are widely used in engineering to deliver fluid from one place to another. There are two types of flow.

Laminar flow (smooth flow) :

Flow in discrete layers with no mixing (Re<2000)

Turbulent flow:

Flow with eddy or mixing action (Re>2000)

Transition region: 2000<Re<4000

(Reynolds Number is used to predict the laminar/turbulent flows)                                                                                                                                         

µ=viscosity

Normally, flow sections of circular cross section are mentioned to as pipes (when the fluid is a liquid), and flow sections of non circular cross section as ducts (when the fluid is a gas).

To pass the liquid used circular cross section pipes, because that can withstand large pressure heads between inside and outside.

Let us consider the velocity profile in a pipe flow.

The fluid velocity of pipe surface is zero, because of no friction. The maximum velocity acting at the center of the pipe. When practically, if the pipe diameter is content, used average velocity.

Head loss in a pipe flow

First, derive a general equation for head loss in a pipe.

The total energy of a fluid (Total Head)         = kinetic energy + potential energy + pressure

                                                                        = P + 1/2v² + Z   ( unit is Pa )

If there is no energy loss,

            Total Head @ 1 = Total Head @2

If there is a head gain in a pipe,

If there is a head gain in a pipe,

** liquids flow from a point of high head to low head.

If the pipe diameter is constant, there have formula to can be directly applied.

This formula called Darcy-Weisbach equation.

h_f  is energy loss

L is the pipe length

v is the mean velocity