Can I replace my 24-inch corrugated pipe with a 21-inch smooth bore plastic pipe?

Most of the time, NO.

The thought is this:
the 21-inch diameter pipe has 30 percent less area, but the roughness is 30 percent less so the capacity should be the same.

However, this is only true for pipes that are fairly long and flat and flowing under outlet control. Culvert pipes less than 60 feet in length are almost always flowing under inlet control and how the water gets into the pipe will control the capacity. A smooth pipe may be less prone to filling with sediment, but also may have too much velocity at the outlet.

Resources

Definitions

Inlet control

A condition where the relation between headwater elevation and discharge is controlled by the upstream end of any structure through which water may flow.

Outlet control

A condition where the relation between headwater elevation and discharge is controlled by the conduit, outlet, or downstream conditions of any structure through which water may flow.

Roadway and Roadside Drainage (pdf)
CLRP workshop manual

June, 2010