I mean that you can try (and have luck) to suppose that a fully develeped turbulent profile (for a pipe) exists and prescribe it if you have some velocity measurement. The cone will allow to let the flow develop towards the nozzle.

I have no other idea than "try and test" ...

I dont have any mesurements of the velocity in the inlet of the cone ( blow dryer) .

Looking at the photo and thinking of a typical hair dryer, I think there are lot of things inside the blower that could create wakes in the flowfield. Therefore, I think that even if you include part of the end cone of the blower in your computational domain, you won't be able to impose a statistically representative quantity for velocity, pressure and turbulent quantities, on the "new" inlet boundary of your simulation.

Considering this, I would suggest to reduce your computational domain: the nozzle you're investigating has a cylindrical shape in the initial part and it seems that a steady flowfield is achieved in it, as long as your measurements are concerned (some diameter after the hair dryer-nozzle junction the exp. velocity is not chaning anymore). I suggest you to cut your computational domain and put the new inlet boundary in the same position where you experimentally observe that the flow velocity within the nozzle is not changin anymore, and then impose the same velocity on the computational boundary (3.15 m/s). I would assume that the wakes have disappeared/dissipated on the new inlet section, at least the bigger.

I agree that an experimental pressure would certainly help to better impose the boundary conditions on your computational domain. You have however to assume turbulent quantities on your inlet boundary, as prof. MFDenaro already wrote, and the best thing you can do to start is assume a fully developed turbulent profile. To verify the impact of this assumption on your CFD3D results, you can re-run your simulation with different inlet turbulent quantities and check how much the results will change (e.g. change turbulence intensity, etc. etc.).

You can also do another thing: add a cylindrical pipe between the blower and the nozzle. The longer the cylindrical pipe the better it is theoretically, but some diameter length will be enough. Then you can measure the velocity profile in the junction between the nozzle and the cylindrical pipe, this way avoiding the wakes coming from the blower. You can measure the velocity in the centerline and near the walls easily there and you don't have any close grid upstream influencing your measurements... If the pipe is long enough, you will have a fully developed turbulent profile in it so you should be able to set turbulent quantities easily in your model (and you don't have to reduce your computational domain).

What it is not clear to me (I don't have enough experience in experimental devices) is if this velocity measurement is accurate or not. For turbulent flow it would requires a very accurate device. And the measures must be statistically averaged to be congruent to the RANS simulation...

Thank you for your suggestions, i did listened to it by using the velocity 3.15m/s at the i let wich was almost constant in the cylindre shape of the nozzle, now the new problem is when the jet exits the nozzle the numerical axial velocity at the exit was almost the same like the experimental data ... Fine, after that it keeps going up for few axial stations then it decays , where in the experimental mesurements there is no going up, the velocity decays the moment it exits the nozzle. Could you help me finding why ?