Sizing Pipe or Orifice to Reduce Flow From an Already Water Flow, Existing Pump.

Use Bernoulli's equation which states that for steady-state flow piezometric pressure (p + gamma * Z) plus velocity head (V*2/2g) are constant between two points.

You don't want this as excess energy for your purpose exists. The plate, flow-throttling, or sudden contractions (due to pipe size reductions) are all methods to cause the flow regime to become "unsteady". The fluid will dissipate fluid energy as heat.

You need to loose significant energy before the fluid enters the heat exchanger.

Another equation needed is continuity Q=VA (not linear for pipes) and only applicable for "steady" flow.

Pick up a hydraulic handbook or tables or grab a nomograph to solve these pipe equations.

There are numoreus flow calc softwares such as this: Pipe flow rate calculation | calculate pipe pressure drop with ...

We need to know the head vs flow characteristics of the pump, the relative elevations of all the items, any requirement of the condenser for entering water pressure, at least a rough idea of pipe sizes and lengths in the overall system, and any pressure gauge readings that may be available.

Temporarily put a water meter in the line you want to control, and have a pressure gauge at the same location. Measure the flow and pressure for all conditions, to get a handle on your situation. Once you have the numbers for max flow and pressure, you can then use standard tables to determine what size orifice will suit your needs.

If it would not clog up with sediment or scale, you might leave the meter in, so you could tell if flow in the system changes, due to scaling, etc.

you can have the impellers machined to pump a lesser value. after you figure out your pipe , fine tune it with the impeller,

You should take several steps to make sure you understand the heat and water flows of the existing cooling water system, and the impacts of the added condensor to the system.

Step one is to make a diagramatic sketch of the system as it now exists. Include any thing you know or can assume for pipe size, flow rate, water temp, and pressure at various system points

Step two is to fill in the heat loads that use the cooling tower capacity, with assumed numbers for heat load, flow rate, and temperatures in and out of the different branch lines.

Third, confirm the pumps and cooling tower do have sufficient capacity to handle the addition of the condensor into the system.

Step four, sketch in the proposed location of the branch supply and return piping for the new condensor. Add in the assumed numbers for heat load, flow rate, and temperatures in and out of the condensor.

Step five is to confirm the new numbers do not compromise existing system operations. If needed iterate with differing flow rates and temperatures to optimize the new system behavior.

Step six, after the desired revised system performance is optimized, begin to size the piping to handle the flow to and from the new condensor. Try to oversize by 10 or 20%, and use butterfly valves at the new condensor to balance and adjust flow as needed.

"How do I reduce the cooling water flow to the desired rate"

Your ultimate aim is to ensure the condenser just the required water and not more, right? You have a valve on the line leading to condenser, as you told. Keep pinching this valve until the condenser cries for water. This should be indicated by the rise of vapor pressure in the condenser. Add a little (say a quarter turn or even less) and ensure the vapor pressure get reduced back to desirable value. This, as you fear, is a temporary solution and an orifice equal to the opening of the valve would be a desirable permanent solution, right?

Suggestion1: Try using a Globe (preferably a 'rising spindle type') valve instead Gate valve, since former has a better control on flow for adjustments. Once you have achieved the right amount of opening, lock the spindle at that position such that you can close but not open further. This can be simple done with two nuts to suit to the spindle thread. And nuts are to be fixed below the valve yoke thread.

This can be adjusted whenever wanted, of course, with tools only.

Suggetion2: Arrange a setup as illustrated. On the downstream of the valve locate a suitable flange joint (if not, avail one) for the insertion of orifice. Keep few approximate sized orifices in steps; say 1", 1.25" and 1.5".

Start with the small orifice. Keep the valve at the desired opening. If the installed orifice has the same area of cross section as that of the valve, the pressure gauges PG1 and PG2 should show the same pressure, right? If PG1 is more than PG2, go for the next sized orifice. In couple of attempts you could achieve near precise orifice. Later you could wide open the valve. Take care that the condenser is not starved heavily during this exercise.