Fluid Dynamics

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TOPIC 5

• Bernoullis Equation- Mechanical Energy Balance

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Mechanical Energy Balance
From the energy equation (4.5) dividing by mass
and assuming incompressible flow
Lets define the friction heating per unit mass
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Mechanical Energy Balance
(5.1)
This is the Mechanical Energy Balance or
Bernoullis equation
By dividing eq. (5.1) with g we obtain the head
form of the Mechanical Energy Balance
(5.2)

• F /g (sometimes symbolized as hL ) is the
  friction or head loss

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Example Pumping n-pentane

• The figure below shows an arrangement for pumping
  n-pentane (r 39.3 lbm/ft3) at 25C from one
  tank to another, through a vertical distance of
  40 ft. All piping is 3-in I.D. Assume that the
  overall frictional losses in the pipes are given
  by the following expression
• (losses) 2.5 V2 ft2/s2 2.5 V2/gc ft.lbf/lbm.
• The pump and its motor have a combined efficiency
  of 75. If the mean (average) velocity, V is 25
  ft/s, determine
• (a) The power required to drive the pump

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Simplifications

• Assumptions
• Steady, incompressible, frictionless (inviscid)
  flow
• No heat transfer or change in internal energy, no
  shaft work
• Single input-output
• Bernoullis equation (5.1) reduces to

(5.3)
In terms of heads (units of length)
(5.4)
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Example Pumping n-pentane (contd)

• For the pumping n-pentane example, shown in page
  5.4 determine
• (b) The pressure at the inlet of the pump and
  compare it with 10.3 psia, which is the vapor
  pressure of n-pentane at 25C
• (c) The pressure at the pump exit
• Note For simplicity you can ignore friction in
  the short length of pipe leading to the pump inlet

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Example Tank Draining (Torricellis equation)

• Consider a tank full of water and open at the
  top. There is a hole near the bottom, the
  diameter of which is small compared with the
  diameter of the tank. Find the velocity of the
  fluid leaving the tank. (The velocity of the
  fluid in the tank itself can be treated as
  negligible).