12. η and ε = f(flow characteristics) => they vary point to point in the flow
13. Reynold’s expression for turbulent shear stress:
• Consider two fluid layers A & B at small distance apart
• Average velocities = and
• Assumption is >
• => Relative velocity of layer A w.r.t B = – = Vx
where Vx = fluctuating component of velocity in X-direction due to turbulence
Let Vy = fluctuating component of velocity in Y-direction
• If over a surface area A perpendicular to y-direction & separating two fluid layers the component Vy are
uniformly distributed => fluid mass transferred across that surface per sec = ρAVy
• Since fluid mass relative velocity is Vx => momentum transfer = ρAVxVy and tangential force development
on each layer
• => corresponding shear stress exerted on fluid layers = τ = Force/Area = (ρAVxVy)/A = ρAVx
• Since Vx & Vy vary hence τ will also vary => time average value is taken
• is known as Reynolds stress
𝑣B
A
B
𝑣A
X
Y
