force acting on fluid hydrodynamically smooth & rough boundaries,applied fluid mechanics
TRANSCRIPT
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….