Consider a fully developed flow of water in a smooth pipe of diameter \(15 \mathrm{~cm}\) at a flow rate of \(0.006 \mathrm{~m}^{3} / \mathrm{s}\).

The pressure drop can be calculated by the Blasius relation for this case.

Verify by an overall force balance that the wall shear stress is equal to \((R / 2)(-d p / d z)\). Use the shear-stress value to find the friction velocity and the length scale near the wall.

Determine the thickness of

(a) the laminar sublayer,

(b) the buffer layer, and

(c) the turbulent core.

Find the local (time-averaged) velocity at a location \(5 \mathrm{~cm}\) from the pipe wall.