Scratching my head over this one, as someone has made me doubt myself.

I will simplify it:

Say I have an air duct (or pipe) with air (or water) flowing in it at a volumetric flow rate of 2m3/s. And say the duct has a cross sectional area of 1m2 (1m x 1m).

The velocity through it will be 2m/s, all good?

Say I put in this duct a heating coil, at right angles to the direction of flow and of Cross sectional area 1m2, the velocity will still be 2m/s

If I then chnage the heating coil to one that is larger and at a 45 degree angle to the direction of flow which spans the whole width of the duct. (say it is 2m2). The Cross sectional area of the heating coil is larger, the volumentric flow rate stays the same.

So does the velocity of the air change? or does it remain the same as the duct that the air is travelling in has not changed its cross sectional area? Only the obstruction within the duct has changed its cross sectional area?

If you start shoving obstructions into the pipe I’d expect the volumetric flow rate to drop unless the pump/fan driving the flow is controlled to increase its power to maintain a constant flow.

yes assume constant flow rate fan/pump

Your first part is correct, however if you are putting something inside the duct then by definition you must be reducing the flow area (the thing inside the duct must take up some space) so the velocity will have to increase.

If I then chnage the heating coil to one that is larger and at a 45 degree angle to the direction of flow which spans the whole width of the duct. (say it is 2m2).

This makes no sense. If your original duct has a cross section of 1m2 then how can you fit a heating coil inside it with a 2m2 flow area?

assume base case is duct with smaller coil at right angles.

what impact will putting a larger coil at an angle have?

Will this increase/decrease or have no affect on velocity?

This makes no sense. If your original duct has a cross section of 1m2 then how can you fit a heating coil inside it with a 2m2 flow area?

at an angle to direction of flow

Are you confusing flow area and heat transfer area?

Basically, if you put something in the duct, the cross sectional area of the duct is reduced, and no longer 1m2. Therefore, for the same volumetric flowrate to go through, it must speed up and travel faster through the obstructed section.

is it on a conveyor belt?

Say I have an air duct (or pipe) with air (or water) flowing in it at a volumetric flow rate of 2m3/s. And say the duct has a cross sectional area of 1m2 (1m x 1m).

are we assuming the duct is square in section?

The averagevelocity through it will be 2m/s, all good?

the velocity the air will vary within the crosssection if it is fully formed turbulent flow

Say I put in this duct a heating coil, at right angles to the direction of flow and of Cross sectional area 1m2, the velocity will still be 2m/s

if you put an obstruction into the airflow it will slow the average airflow velocity down, the air need to pass around the obstruction

And don’t forget that once you turn your heating coil on, the air will warm up and expand, which will put the cats rights in with the pigeons 🙂

Say I put in this duct a heating coil, at right angles to the direction of flow and of Cross sectional area 1m2, the velocity will still be 2m/s

If the duct has a CSA of 1m2, and the heating coil has a CSA of 1m2, the coil will completely block the duct anyway, so there will be no flow.

These are all very hypothetical numbers so dont focus on the figures too much.

Is v2 the same or different to v?

If the duct has a CSA of 1m2, and the heating coil has a CSA of 1m2, the coil will completely block the duct anyway, so there will be no flow.

Assume the coil has a free area of 50%, air passed through it. and it is the speed of this air I am interested in.

which will put the cats rights in with the pigeons

Have you ever tried to put a cat somewhere it doesn’t want to go?

I’d just ut a mesh over the end personally

Ignoring coil areas, from what you have drawn the velocity in the duct in both cases will be 2 m/s BUT the local velocity at the coils will be higher. How much higher depends on the way the coil is arranged.

Given the other uncertainties here I doubt we have to worry about entry length, boundary layers, or even the temperature rise.

you need to look at his in small sections. In the 1st case you have a single reduction in area. so if your volume flowrate is constant but your area is halved, then velocity is increased.

With the angled coil, a a whole load of assumptions come in for simplification. But we did a bundle of those earlier anyway.

For he angled coil, think of them as a series of bars. clearly if they were widely separated, you would have minimal contraction and so velocity would increase but not greatly. with small separation you have a similar effect, assuming ideal fluid, which is mathematically ok, but in real terms not.

in reality you would have all kind of flow conditions, boundary layers, vortex streets, laminar turbulent transitions, that the idea of velocity is a bit meaningless. it would vary throughout the region of interest.