CE 230-Engineering Fluid Mechanics

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CE 230-Engineering Fluid Mechanics
Fluid flow
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Flowing fluids

• Static versus flowing fluid
• Objectives of the part of course
• Basic concepts and definitions

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Types of flow

• Steady versus unsteady
• Uniform versus no uniform
• 1-D versus multi-D
• Laminar versus turbulent

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Development of flow pattern

• Why not solve problem?
• Flow visualization analog and experimental
  methods
• Streamlines, streaklines and pathlines

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Pathlines
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Uniform flow
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Non-uniform flow
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Velocity distribution in a pipe- laminar vs
turbulent flow
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Volume flow rate, Q

• Q ?V/ ?t dV/dt
• Calculating Q if velocity is constant
• Q? v.dA
• Mass flow rate

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Example 5.3
Find flow rate and average velocity in the pipe
(R5 cm), if the velocity distribution is given
by Note that U cm/s r cm
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Example 5.3
Find flow rate and average velocity in the 5 m
wide channel. Given d 2 m and maximum velocity
3 m/s.
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Example
Find flow rate and average velocity in the
triangular channel. Given maximum velocity 6
ft/s.
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Material derivative and Acceleration

• Total acceleration
• Local acceleration
• Convective acceleration

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Example (p 4-26)
Determine local, convective and total
accelaration at x0.5L and t 3 s
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BERNOULLI EQUATION
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Derivation of Eulers equation

• Consider a cylindrical fluid element being
  accelerated in direction l and neglect viscous
  effects
• Use equilibrium equation
• S F m a

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Derivation of Eulers equation
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Lets take l along a stream line call s (i.e.
flow along a streamline)
But
Therefore
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Assume steady flow and drop subscript
But last term is
Substituting back, dividing by ? (assuing
incompressible fluid) and integrating wrt s we
get
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Bernoulli equation
One form of BE is
Note assumptions made No losses Flow along
streamline Steady flow incompressible
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4.44 Consider water jet shown. Calculate h, if
the water velocity as it exists the nozzle is 20
ft/s
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4.103 Find pressure at A if h15 m and V6 m/s
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Estimate exit velocity and minimum pressure
L
H
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Stagnation tube
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Find flow rate of water given pipe diameter at 2
10 cm pipe diameter at 1 30 cm
5 m
60 cm
Hg
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4.64 Find V and Q
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5.76 Find manometer deflection
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Pitot tube