Viscous Flow in Ducts Computation of Discharge Coefficient in Butterfly Valve

1
Viscous Flow in DuctsComputation of Discharge
Coefficient in Butterfly Valve

• John Grady
• David Ramezani
• Austin Thompson

Problem 6.160 BIEN 301 February 14, 2007
2
Problem

• Given
• The butterfly-valve losses may be viewed as a
  type of Bernoulli obstruction device. The "throat
  area" can be interpreted as the two slivers of
  opening around the butterfly disk when viewed
  from upstream.

3
Problem

• Asked
• Fit the average loss Kmean versus the opening
  angle to an exponential curve.
• Use your curve fit to compute the "discharge
  coefficient" of a butterfly valve as a function
  of the opening angle.
• Plot the results and compare them to those for a
  typical flowmeter.

4
Assumptions

• Incompressible flow
• Liquid
• Laminar flow

5
Opening Area

• The opening area of the butterfly valve was found
  to be a function of the opening angle and the
  diameter of the pipe.

6
Loss Coefficient Equation

• A curve fit was used to find an equation for K
  from Figure 6.18b

7
Loss Coefficient Equation
8
Discharge Coefficient

• The formula for discharge coefficient was derived
  from equation 6.104

9
Discharge Coefficient

• To reduce the discharge coefficient equation to
  an equation involving K and ß only equation 6.78
  was used.

10
Discharge Coefficient

• The discharge coefficient equation becomes
• where ß is the ratio of the partial area to the
  full area.

11
Discharge Coefficient

• After substituting the found values, the final
  discharge coefficient equation, as a function of
  the opening angle, was found to be

12
Graph of Discharge Coefficient
13
Biomedical Application

• The process used in determining the discharge
  coefficient of the valve described in this
  problem could be applied to calculations
  regarding the heart. Since loss would be
  different in every heart, it may become necessary
  for a doctor to determine if a heart is
  functioning correctly, or in the design of a
  future prosthetic heart.