For a typical hydroelectric dam, kinetic energy is not particularly important (although smaller kinetic hydroelectric plants do exist). The relevant factors are pressure (determined by the hydraulic head) and volumetric flow.
In ideal conditions, if you have two sections of identical pipe, and a turbine in the middle, water flowing through the pipe will not change velocity (incompressible fluid, and none is gained or lost), yet the turbine can harvest one Joule per cubic metre per Pascal of pressure.
This is the predominant principle by which a dam works; it creates a large pressure differential, and then drives a turbine at a relatively much slower velocity than the maximum possible by converting all the GPE to KE.
To adapt this to your chutes idea. Water will not pour down the longer chute significantly quicker than the shorter one, yet if you fill them, the longer chutes will have a proportionately larger pressure at the bottom. Thus a flow of 1m^3/s will deliver proportionately more energy across a turbine which reduces the pressure to ambient.
In ideal conditions, if you have two sections of identical pipe, and a turbine in the middle, water flowing through the pipe will not change velocity (incompressible fluid, and none is gained or lost), yet the turbine can harvest one Joule per cubic metre per Pascal of pressure.
This is the predominant principle by which a dam works; it creates a large pressure differential, and then drives a turbine at a relatively much slower velocity than the maximum possible by converting all the GPE to KE.
To adapt this to your chutes idea. Water will not pour down the longer chute significantly quicker than the shorter one, yet if you fill them, the longer chutes will have a proportionately larger pressure at the bottom. Thus a flow of 1m^3/s will deliver proportionately more energy across a turbine which reduces the pressure to ambient.