Static Pressure(s) Along a Cross-Section of a Duct

I think you may be confusing terms here, specifically static pressure , dynamic(or velocity) pressure and total pressure....

https://www.captiveaire.com/MANUALS/AIRSYSTEMDESIGN/DESIGNAIRSYSTEMS.HTM

I agree with SE and dhayanandhan, and what they suggest is totally correct in a smooth uniform duct. Here is my off to the side question:

Suppose a home HVAC system set of air ducts branching off an air-handler. Fan forces air up through the furnace/AC coil to heat or cool the house. There is a net positive dynamic pressure in the ducts, otherwise no air movement. The question is this: will irregularities coupled with pinhole leaks in the air duct produce a Bernoulli effect induction of outside air and dust into the streaming air duct? I think it will.

We had noticed that our older house has always been a particularly dusty home even for West Texas (where fine silt collects in attic during lahar dust storms). Even though the ducts are wrapped with typical fiber glass duct insulation with outer cloth sleeve, I have long thought we are getting dust infiltration from the attic. Yesterday, we had new insulation blown in the attic, and by Mesmer effect, or reality, we seem to be breathing better. And by the way, heater never cycled on all night.

I can't agree with that. There is static pressure also when fluid is flowing. It is usually measured from a simple tapping in the pipe wall. Static pressure is to be distinguished from the dynamic pressure 0.5*ρ*V². Sum of the two = total pressure.

Velocity Profile is parabolic (in circular pipe) only for laminar flow. OP didn't give flow details, but laminar flow is rare in practice. In turbulent flow the velocity is fairly constant across the pipe width.

To answer OP's question, I believe if static pressure were measured with a tube protruding into the pipe instead of a wall tapping (tube dia << pipe dia to avoid disturbing the flow), the reading would be the same, and constant across the pipe width, in laminar or turbulent flow. But I can't say I've ever tried it, and others may comment.

You may be right as I still have had no opportunity to try it - although I possess gas manometers.

Yupp, static is when nothing flows. So it will be all the same.

Over the cross section you will get some differentiation of pressure when flowing, but the overall impact on the system is given on the ends and as you already stated from the flow regime. Turbulent will give you more friction.

My fault was not putting it straight

I meant measurement of a fan flow by tranducer converting differential SP into the flow (for that type of fan according to its working curve)

May not SP, taken by the pipes, differ depending on how deep the pipes are inserted ? Just near the surface (thanks for correcting me, where the flow is more laminar), as compared to a deeper position (where flow should always be more turbulant)

Once again, SP (static pressure) is measured at zero flow, zero velocity. It does not matter where the pressure probe is located with respect to axial of longitudinal position in the duct.

SP does not exist when the flow is >0, because the system is not static. Dynamic pressure, as a result of friction or resistance to air flow matters and changes with respect to axial (or radial) position within the duct, and also longitudinally, since friction accumulates with length of duct.

Now this was not straight either.

Are you refering to the air pressure gradient as in atmosperic pressure?

If your pipes are vertical then the cross section pressure will be different by a bit for all given sections due to the air pressure gradient.

What do you really need to know?