(Solved): ASAP Hydropower of in-stream turbines (metric units) n=20 in-stream water turbines with a radius of ...

Hydropower of in-stream turbines (metric units) $$n=20$$ in-stream water turbines with a radius of $$R=1.5[\mathrm{m}]$$, drag coefficient $$c_d=0.5$$ mechanical efficiency $$?=0.9$$ are placed in a river across its cross-section that flows at $$U=2.1\left[\mathrm{m}{\mathrm{s}}^{?1}\right]$$ velocity and delivers $$Q=A_{\text{riviur }}U=2600\left[{\mathrm{m}}^3{\mathrm{s}}^{?1}\right]$$ flow. The density of water is $${?}_{\text{uut }}=1000\left[\mathrm{kg}{\mathrm{m}}^{?3}\right]$$ a) Calculate the horizontal force that the river will impose on the turbines $$\left(F_d=\frac{1}{2}{c}_d{?}_{\text{wat }}{A}_{turb}{U}^2\right)$$. b) Calculate the power that each turbine will extract from the river $$\left(P_{turb}=F_{d}U\right)$$. c) Calculate the power the $$n=20$$ turbines will generate after counting its mechanical efficiency. d) Calculate the power of the water flowing in the river. The mass flowrate of the river is $$\stackrel{?}{m}=$$ $${?}_{zat}Q$$ and the power of that mass flow-rate is given by $$P_{\text{riter }}=\frac{1}{2}m{U}^2$$. e) Calculate the velocity of the river after the in-stream turbine. Solution: