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Fluid Dynamics


Example: Tank Draining (Torricelli's equation) Consider a tank full of water and open at the top. ... Find the velocity of the fluid leaving the tank. ... – PowerPoint PPT presentation

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Title: Fluid Dynamics

  • Bernoullis Equation- Mechanical Energy Balance

Mechanical Energy Balance
From the energy equation (4.5) dividing by mass
and assuming incompressible flow
Lets define the friction heating per unit mass
Mechanical Energy Balance
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
  • F /g (sometimes symbolized as hL ) is the
    friction or head loss

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

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

In terms of heads (units of length)
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

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
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