calculate the momentum deficit correction factor.

CONSERVATION OF MOMENTUM (OPEN SYSTEMS)  INTEGRAL CONTROL VOLUME APPROACH

  eeiiCVCV vmvmFdt )vm(d 



Applicable to systems with uniform  velocity distribution at inlets and outlets. 

CARTESIAN COORDINATES 

( ) ( ) ( ) ( )

( ) ( ) ( ) ( )

( ) ( ) ( ) ( )

x CV x CV i x i e x e

y CV y CV i y i e y e

z CV z CV i z i e z e

d mv F m v m v

dt d mv

F m v m v dt

d mv F m v m v

dt

  

  

  

  

  

  

 

 

 

For systems with non‐uniform velocity  distribution at inlets/outlets:

( )CV CV i i e e

d mv F v v dA v v dA

dt         

      

Study examples 6.9‐6.12

( ) ( ) ( )CV CV avg in avg out

d mv F m v m v

dt      

     2 2

1

1

avgv v v dAA v

dA A v



  

    

 









Or equivalently,

Table 6.1

JvWaterjet

Circular diskD

?F 

A constant jet of water exits a nozzle of diameter D=15mm and strikes a disk held perpendicular to the jet. After striking the disk, the water jet spreads symmetrically over the disk surface in the radial direction. Assuming that atmospheric pressure acts uniformly over the back side of the disk and through the jet cross section at the nozzle’s exit, determine

a) The horizontal force required to hold the disk stationary if the water velocity profile exiting the nozzle is uniform and constant at vJ=12m/s.

b) The horizontal force required to hold the disk stationary if the water velocity profile exiting the nozzle is laminar at vJ=vmax=12m/s. (What if the jet was turbulent at n=1/7 and vmax=12m/s?)

c) The net force opposing the disk motion if the disk is moving with a constant speed of 3.2m/s to the right with respect to a stationary observer. The water jet speed is uniform and maintained at 12m/s.

CONSERVATION OF MOMENTUM (OPEN SYSTEMS)  INTEGRAL CONTROL VOLUME APPROACH‐‐ EXAMPLE