Water at flows at a rate of through a horizontal pipe of 0.1m diameter. The pressure gradient is measured to be 2.5kPa/m along the length of the pipe. Determine: (i) approximate thickness of the viscous sub-layer; (ii) approximate centerline velocity; (iii) ratio of the turbulent to laminar shear stress at a point midway between the centerline and pipe wall. Take density and kinematic viscosity of water at as and respectively
Solution :
Irrespective of the flow to be laminar or turbulent, the shear at the wall can be obtained from the equation as,
Friction velocity is given by,
Approximate thickness of viscous sub-layer is given by,
flows at a rate of 
through a horizontal pipe of 0.1m diameter. The pressure gradient is measured to be 2.5kPa/m along the length of the pipe. Determine: (i) approximate thickness of the viscous sub-layer; (ii) approximate centerline velocity; (iii) ratio of the turbulent to laminar shear stress at a point midway between the centerline and pipe wall. Take density and kinematic viscosity of water at 
and 
respectively
