Problem 4.2.1

 

Water is flowing through a pipe.  A number of flow measurement devices are available.  Those include orifice, nozzle and venturi. 

Flow meter coefficient, C, is dependent upon Reynolds number.  For orifices and nozzles, Reynolds number is based on larger diameter (pipe diameter).  For venturis, Reynolds number is calculated using smaller diameter.

 

Nozzles:  As we do not know the value of nozzle coefficient, one can assume turbulent flow condition.  Nozzle coefficient is plotted as function of Reynolds number and beta, where beta is ratio of nozzle diameter to pipe diameter.  The following procedure is recommended.

 

  1. Assume turbulent flow, and read the value of C for corresponding beta value.
  2. Calculate mass flow rate, w, using the formula: C A1 square root of 2 gc delta P rho.  A1 is the cross-sectional area of the nozzle.
  3. Verify if the assumed value of flow coefficient, C, is correct.
  4. Calculate volumetric flow rate, q using the density of fluid..
  5. Use, pipe diameter, d2 to calculate Reynolds number.  
  6. Calculate cross-section area of the pipe, A2.
  7. Divide q by A2 to obtain V2.
  8. Calculate Reynolds number, V2 d2 rho by mu.
  9. Read the value of C using beta and Reynolds number.
  10. Repeat these calculations with revised value of C, till the solution converges.

 

For the given situation, mass flow rate through nozzle is found to be 5.09 pounds per second. 

 

Similar approach is used for orifice.  Note the chart provided is for a square-edged orifice.  For orifice mass flow rate is found to be 3.54 pounds per second.     

 

For venturis, Reynolds number is based upon d1.