Transcript Pharos University Fluid Mechanics For Electrical Students

Pharos University
ME 259 Fluid Mechanics For
Electrical Students
Lecture # 4
Fluid Flow
Dr. A. Shibl
Viscosity
• Dynamic Viscosity
 = Shear Stress/Slope of velocity profile
F/A
v/ y
Pa-sec
n
F
y
• Kinematic Viscosity
v
Slope = v/y



m2/Sec.
Basic Laws
• Conservation of mass: dM/dt=0 for system
∂/∂t ∫ ϱ d𐐏 + ∫ ϱ ⊽. d Ᾱ =0 for control
vol.
• Newton’s 2nd law Σ F = ma
Σ F = ∂/∂t ∫ ⊽ ϱ d𐐏 + ∫ ⊽ ϱ ⊽. d Ᾱ
• First Law of Thermo: Q - W = dE/dt
Q-w=∂/∂t∫e ϱ d𐐏+∫(p/ ϱ +0.5V2+gz)ϱ⊽. dᾹ
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Continuity in Fluid Flow
• Continuity for any fluid (gas or liquid)
– Mass flow rate In = Mass Flow Rate out
– M1 = M2
M1
– 1*A1*v1 = 2*A2*v2
• Continuity for liquids
– Q1 = Q 2
– A1*v1 = A2*v2
M2
Total Energy and Conservation of
Energy Principle
• E = FE + PE + KE
v2
E  w  w z  w

2g
P
• Two points along the same pipe:
E1 = E2
• Bernoulli’s Equation:
wv12 wp2
wv22
 wz1 

 wz2 

2g

2g
wp1
v12
P2
v22
 z1 

 z2 

2g 
2g
P1
Torricelli’s Theorem
• For a liquid flowing from a tank or
reservoir with constant fluid
elevation, the velocity through the
orifice is given by:
v2 
2 gh
h
where, h is the difference in
elevation between the orifice and
the top of the tank
Example: If h = 3.00 m, compute v2
Momentum Analysis of Flow
Systems
Newton’s Laws
• Newton’s laws:
– First law: a body at rest remains at rest, and a body in motion
remains in motion at the same velocity in a straight path when
the net force acting on it is zero.
– Second law: the acceleration of a body is proportional to the net
force acting on it and is inversely proportional to its mass.
– Third law: when a body exerts a force on a second body, the second
body exerts an equal and opposite force on the first.
Choosing a Control Volume
• Fixed, and moving.
– For moving CV, use
relative velocity,
Body and Surface Forces
Linear Momentum Equation
• Use RTT to shift from system formulation of the
control volume formulation
Special Cases
• Steady Flow
• Average velocities
Reynolds Number
• Describes if the flow is:
– Laminar – Turbulent -
14
Osborne Reynolds Tests
Laminar
Turbulent
15
Real Systems
• Friction losses: As fluids flow in pipes
• Minor losses: due the presence of valves, elbows,
pipe entrance, etc.
• Motors: Turbines, actuators, etc. take energy from
fluid
• Pumps: Put energy into the fluid
• The Bernoulli equation does not take these losses or
gains into account