present

APPLIED FLUID MECHANICS

Manisha KachadiyaGuided:-

Civil:-6th B

I. Force acting on Fluid II. Hydrodynamically Smooth &

Rough boundariesTopic:-

MAHAVIRSWAMI COLLAGE OF ENGG. & TECH.

Savani MilanRathod RasheshVegad Kartik

141110106081141110106078141110106095

PARTICIPATED STUDENTS

The various forces that may influence the motion if a fluid are :-

Gravity Force, Fg or body force Pressure Force, Fp Viscous Force, Fv Turbulent Force, Ft Surface tension Force, Fs Compressibility Force, Fe

FORCES ACTING ON FLUID IN MOTION

It is due to the weight of the fluid.

:. Fg = m.g

I. Gravity Force, Fg or body force

It is due to pressure gradient between the points in the direction of flow

II. Pressure Force, Fp III. Viscous Force, Fv

It is due to Viscosity of the flowing fluid, and thus exists in the case of all real fluids.

It is due to turbulent of the flow. In the turbulent flow, the fluid particles move from one layer to

other and therefore, there is a continuous momentum transfer between adjacent layers, which results in developing additional stresses called Reynolds stresses.

IV. Turbulent Force, Ft

It is due to the cohesive property of the fluid mass. It is however, important only when the depth of flow is very small.

V. Surface tension Force, Fs

It is due to the elastic property of the fluid and is important only when fluid is compressible.

VI. Compressibility Force, Fe

If a certain mass of fluid in motion is influenced by all the above mentioned forces then according to Newton’s law of motion, the following equation of motion may be written;

Ma = Fg + Fp + Fv + Ft + Fs + Fe

Further resolving these forces in x, y and z direction:

Max = Fgx + Fpx + Fvx + Ftx + Fsx + Fex

May = Fgy + Fpy + Fvy + Fty + Fsy + Fey

Maz = Fgz + Fpz + Fvz + Ftz + Fsz + Fez

where M is the mass of the fluid and ax, ay and az are fluid acceleration in the x, y and z directions respectively

In most of the fluid problems Fe and Fs may be neglected, hence

Ma = Fg + Fp + Fv + Ft • Then above equation is known as Reynold’s Equation of Motion

For laminar flows, Ft is negligible, hence

Ma = Fg + Fp + Fv

• Then the above equation is known as Navier Stokes Equation

In case of ideal fluids, Fv is zero, hence

Ma = Fg + Fp

• Then the above equation is known as the Euler’s Equation of Motion

INTRODUCTION: Laminar Flow: In this type of flow, fluid particles moves along smooth straight

parallel paths in layers or laminas, with one layer gliding smoothly over an adjacent layer, the paths of individual fluid particles do not cross those of neighbouring particles.

Turbulent Flow: In turbulent flow, there is an irregular random movement of fluid in transverse direction to the main flow. This irregular, fluctuating motion can be regarded as superimposed on the mean motion of the fluid.

Hydrodynamically smooth &

rough boundaries

Laminar

Transitional

Turbulent

Types of flow depend on the Reynold number , ρVd Re = -------- µ Re < 2000 – flow is laminar

Re > 2000 – flow is turbulent

2000 < Re < 4000 – flow changes from laminar to turbulent.

Hydrodynamically rough pipe :

• The hight of roughness of pipe is greater than the thickness of laminar sublayer of flowing fluid.

• K > δ′

Hydrodynamically smooth &

rough boundaries Hydrodynamically smooth

pipe :• The hight of roughness of pipe is less

than thickness of laminar sublayer of flowing fluid.

• K < δ′

Criteria for roughness:• Hydrodynamically smooth pipe • Hydrodynamically rough pipe• Transition region region in a pipe

From Nikuradse’s experiment

25.0k

6k

625.0

k

In terms of Reynolds number

1. If Re <4 → Smooth boundary2. If Re ≥100 → Rough boundary3. If 4<Re <100 → Boundary is in transition stage.

Velocity Distribution for turbulent

flow Velocity Distribution

in a hydrodynamically smooth pipe

Velocity Distribution in a hydrodynamically Rough Pipes

y

Vv

elog5.25.8*

R

Vv

elog5.275.4*

Velocity Distribution for turbulentflow in terms of average Velocity (V)

Velocity Distribution in a hydrodynamically smooth pipe

Velocity Distribution in a hydrodynamically Rough Pipes

RV

VV

e

*5.275.1* log

R

VV

elog5.275.4*

THANK YOU….