Open Feed Water Mixer Questions

We're currently studying the rankine regenerative cycle this semister. I have two main questions here:
1. Can you have and open feed water mixer with out using two pumps? (I've googled this and it doesn't show any rankine cycles without the use of two pumps. The problem is that our Dr. suggested that you can let the portion of steam leaving the turbine mix directly in the heater with the liquid leaving the condensor. And that the pressure of the resulting steam is the net average of the pressure of both steams: P3=(P1+P2)/2), this brings me to my second question).

2. I have stream of vapour with a mass flow rate of Y and pressure P1. It's mixes directly with another stream of liquid with a mass flow rate of Z and pressure P2. Will the resulting stream have a pressure of P3=(P1+P2)/2? (Presuming they mix in a normal Open Feed Water Heater)

If anyone can give me links that might answer any of my question, or answer them personally I'll be much obliged.

Ps: (I've tried using this site: http://www.postmixing.com. But it's not working at the moment)