Download ChE 345 Chemical Engineering Fluid Mechanics

BERNOULLI EQUATION
Bernoulli’s presenter:
Fan Chao Way
Nur Suhaili Mohd Yatim
Nurirdayu Jantan
Nurul Maisyarah Samsudin
POTENTIAL ENERGY
• Due to its elevation, the potential energy of
the element relative to some reference level
• PE = wz
w= weight of element
z= elevation
KINETIC ENERGY
• Due to its velocity, the kinetic energy of the
element is:
• KE=wv2/2g
FLOW ENERGY
• Pressure energy or flow work
• Represent the amount of work to move the
element of fluid across the certain certain
section against pressure.
• FE = wp/γ
• The force on the element is pA, where p is the
pressure at the section and A is the area of the
section.
• In moving the element across the section, the
forces moves, the force moves a distance L
equal to the length of element.
• Work = pAL =pv
• Where the v is the volume of the element.
• The weight of the element w is
• W = γV
•
•
•
•
Where γ is the specific weight of the fluid.
The volume of the element is
V = w/ γ
So work =pv = pw/ γ
6.7 INTERPRETATION OF BERNOULLI’S
EQUATION
Each term in Bernoulli's equation is one form of
the energy possessed by the fluid per unit
weight of fluid flowing in the system.
Unit in each term Energy per unit weight
In SI system : N.m
N
In customary system : Ib.ft
Ib
In fluid flow analysis, the term are typically
expressed as “head” referring to a height
above a reference level. Specifically,
p/γ= pressure head
z = elevation head
V2/2g= velocity head
Total head = p/γ(pressure head) +z (elevation head) +
V2/2g(velocity head)
Point 1-2 : magnitude may change in value
• No energy lost/added, total head remains
constant level.
• Continuity equation: A1v1 = A2 v2
v2 = v1(A1/A2)
• v2< v1
• A1<A2, v2< v1, so v22/2g<v12/2g
• Pressure head ↑ because velocity head ↓
6.8 RESTRICTION ON BERNOULLI’S EQUATION
1.Valid only for incompressible fluids because the
specific weight of the fluid is assumed to be the same
at the 2 sections of interest.
2.No mechanical devices between the 2 sections of
interest that would add energy to or remove energy
from the system, because the equation states that the
total energy in the fluid is constant.
3.No heat transferred into or out of the fluids.
4.No energy lost due to friction.