Flow with Friction

  M V p T r a h p0 T0 r0 a0 h0
M<1 ↑  M→ 1 ↑ ↓

↓

  

↓

↓ ↓

no change

   no 
change		 no change
 

friction results in s↑, more democracy!
perfect democracy when KE due to V = KE due to T, or when M=1.  This results in less interference between the particles.

Follows the changes in M.  Also, friction reduces Aeffective of the flow, which increases V when M<1 and decreases V when M>1

Always opposite to the variation in V just like in incompressible flow.  As the flow decelerates: conversion of KE to pressure E (or dynamic E) and vice versa, just like in a spring.

 Opposite to the variation in V (from the E equation)    Follows the variation in T Follows the variation in T h=cpT Friction robs the flow from E.  Since T0 stays the same, p0 must decrease. No heat exchange with surroundings (adiabatic flow)   Follows the variation in T0

Follows the variation in T0 h0=cpT0

 
M>1 ↓   M→ 1 ↓ ↑

↑

  

↑

↑

 ↓

no change

   ↑ ↑