Hello,
My team of students & I are currently working on a concept for a new type of dishwasher. The concept requires a system, which is able to pump high-pressure water through a large number of holes/nozzles, that are distributed equally over a plate.
Our issue regards how to distribute the water-flow equally across the nozzles.

The flow is vertical and pumped from the bottom - and it has to be sprinkled with high pressure. Is it possible to create a manifold with a slope edge, that ensures the pressure and therefore also amount of water/flow is equally distributed? If so, where can i find some theory explaining how to calculate the shape of the manifold?

If there is no flow, the pressure will be constant throughout the manifold (assuming the outlet surface is level).

As soon as water starts to flow through the manifold, the pressure will reduce the further you get from the inlet. Tinkering with the shape of the manifold may change the shape of the pressure distribution but it wonâ€™t stop it falling as you get further away from the inlet.

Two things you can try: First is to make the cross-section of the manifold large relative to the total area of all the nozzles to bring you closer to the no-flow case. The other is to design the manifold with multiple inlets so thereâ€™s less difference in the distance between nozzles and their closest inlet.

Have you decided how youâ€™re going to deal with entrained particulates? The flow through the nozzles will stop being identical the moment one of them gets blocked - and a flat manifold with many holes sounds like a real pain to clean.

You may be overthinking this.
Some questions:
What is the minimum pressure that you need at the nozzles?
What is the maximum pressure that you can accept?
What is the pressure that you want your pump to develop?
Equal pressures and pressure drops:
If the manifold cross section is large in relation to the cross sections of the nozzles the pressure difference between nozzles will be negligible.

Iâ€™m sure you have Googled â€śflow distributionâ€ť to research this topic. Also, Google â€śflow maldistributionâ€ť. It should give relevent information.

Flow distribution is dependent on Ar, the ratio of total nozzle flow area to supply plate/pipe flow area. If one keeps Ar < 0.5, the % maldistribution will be < 5%, which in my experience is the usual minimum design of maldistribution. Here is a graph based on the supply being pipe:

10% maldistribution may be objectionable.

The graph confirms replies from WaRoss and zeusfaber.

Have you and your team had a course in fluid dynamics yet?