Problem $2.[3$ pts$]$

You have been asked to conduct flume experiments to examine the dissolution of chemical from the bed under conditions of smooth turbulent flow. You begin by measuring the velocity profile shown below.

a$.$ Assuming that the flume cannot be truly smooth, but has some roughness of scale, d$.$ What does it mean to have smooth turbulent flow.

b Determine whether the flow is smooth or rough turbulent.

c$.$ Estimate the laminar sub$-$layer thickness, ${}_s.$

d$.$ Sketch the pattern made by a streak of dye released at $y<msub><mrow><mi></mi></mrow><mrow><mi>s</mi></mrow></msub>$ and $y>{}_s.$