... Yes, it is true at high speeds.But losses are caused only due to turbulence, which also occur in a simple pipeline.
In a pipeline the velocity profile across the diameter is approximately parabolic. I.e. at the walls of the pipe the velocity (and hence the wall friction) goes to zero. In your design the velocity at the circular wall is maximum - a lot more wall friction.
... Energy balance is:kinetic energy of water from exit the turbine is subtracted from the initial potential energy. With approximately we can say that:kinetic energy of the water from the turbine entry minus kinetic energy of the water from the exit is equal to the energy ceded.
So to increase the system efficiency should be reduced water velocity at the exit. This is not possible to the systems which have turbines.
No, having the turbine exit KE be essentially zero is possible and is done, at least in the Pelton type turbines.* The KE of the water leaving a Pelton turbine is essentially zero. I.e. it just falls down as the spoon-like cups it collided with move away at the tangential speed of the turbine.
Relative to the ground the water enters the cups at velocity V and they reduce the water velocity to zero, relative to the ground. Stopping the momentum of the entering water requires a force which is supplied by the cups. The third law "reaction force" acts on the cups making the torque that the common shaft applies to the generator, and this shaft is turning at high speed, as the electrical generator requires to be efficient.
... To understand what I want, for a water height of the dam,the water velocity from the exit of the energy receiving system(rotary piston), at constant flow, to be as small as possible.
That means a high capacity rotary piston and low speed.
Yes that low rotational speed will reduce your turbulence losses BUT now you can not directly drive the spinning electrical generator with the same shaft. The electrical generator needs to be turning at high speed to be efficient. You will need some "step up the RPM" gears between your engine and the generator.
If your application did not require high RPM shaft, then your system may have an advantage. For example, it could slowly turn a large grind stone to convert wheat into flour, as water power did 100+ years ago. Back then they needed gears to slow the shaft RPM down. I.e. in this application, yours could be the cheaper system, IF the large volume of its circular chamber did not cost too much to make.
Effectively, in the electric generation application, you reduce the turbulence losses but will introduce new gear losses. I may be wrong, but I suspect that the new gear losses will be greater than the reduction in turbulence losses; but I am certain high speed step up gears, rated for the full peak power, cost a lot of money, which the direct drive water turbines now in use do not need pay.
*As water is essentially incompressible, the product of the flow velocity and the cross section of the tube it is passing thru is a constant. If you look at the typical turbine cross section, you will note that it is small at the entrance and large at the exit. For example if this cross section ratio is 1 to 5 then the exit velocity is 0.2 of the entrance velocity, but the KE is goes as the square of the velocity thus (0.2)^2 = 0.04 or 4% of the entering KE was not captured. That is how large turbines get greater than 90% of the energy captured. Thus, even in non-impulse type turbines, very little KE is left in the exit water, (not captured).
The Pelton and and other type impulse turbine can in principle leave zero KE in the exit water but they do have more friction losses as the water must slide around the cup surface with high speed relative to the cup wall surface as its velocity is reduced to zero, with respect to the earth. In these turbines, the water does not "leave the turbine blades" - Instead the turbine blades leaves the zero velocity water, which just falls down to get out of the way of the next blade rotating into the entering water jet. (That is slightly false as the cups are slightly tilted downward to help the water quickly leave, get out of the way, by more than gravity alone can do.)
One might also note that your design has a relatively small exit opening so the velocity thru it must be very high. I.e. you will leave a lot of KE in the exiting fluid. That is why your design may work well as a jet-ski pump.
Again, let me state I am impressed by your new engine/pump design. Especially the simple machining requirements and few moving parts. I just cannot let you make false claims for it, especially about its efficiency, which will be low compared to other designs for reasons I have discussed.