Some ideas that might help...
What you haven't got yet is the equation for the force of the water hitting the scales.
This will be given by the velocity of the water (meters per second) multiplied by the mass flow (kg per second).
The velocity of the water will obviously depend on the height of the funnel above the scales.
This means that there will not be a single answer,
you can get the same result for a small mass flow from a great height or a large mass flow from a small height.
For simplicity you might want to choose a height that results in a terminal velocity of 1 m/s, you then want to have an initial mass flow of .98 kg/s.
You also want to finish with .98 newtons or a tenth of a kg of water on the scales.
one litre of water masses 1 kg, so the volume of water is 1/10 litre,
this fixes the volume of the funnel, which means that if you choose an initial depth for the water in the funnel, the radius follows.
