Shear Stress due to Laminar flow

[ice87]

Homework Statement

Oil of Density 888kg/m^3 and viscosity 0.8Pa*s is flowing in a horizontal pipe of diameter 0.15m. The local flow velocity at the centerline is 10m/s. find the shear stress exerted by the oil on the wall of the pipe.

Homework Equations

tau = -eta*(dv/dy)

The Attempt at a Solution

= -0.8*(10/0.075) = 106.7 Pa
but the given solution is 213Pa, exactly twice my answer, what am I doing wrong? thanks

 

[AlephZero]

The velocity gradient is not constant across the pipe, so the average gradient (which you calculated) is not the same as the gradient at the pipe wall. See http://www.engineersedge.com/fluid_flow/flow_velocity_profiles.htm

 

[radou]

As AlephZero stated, you should find a velocity function v(y) as a polynomial of degree 2 satisfying the given velocity condition in the middle streamline.