Hydroelectric Power Plant

Question 1

Gross head, h_g

Answer 1

h_hw-h_tw

h_hw = head water elevation
h_tw = tail water elevation

Question 2

Friction Head Loss, h_f (darcy)

Answer 2

[fLV^2]/[2gD]

Question 3

Friction Head Loss, h_f (morse)

Answer 3

[2fLV^2]/[gD]

Question 4

Net head or effective head, h

Answer 4

h_g-h_f

Question 5

Penstock Efficiency, e_p

Answer 5

h/h_g

Question 6

Volume Flow Rate of Water, Q

Answer 6

A*v

A=area of penstock
v=velocity of water

Question 7

Water Power, WP

Answer 7

γQH

γ=9.81 kN/m^3

Question 8

Turbine Efficiency, e_t

Answer 8

[brake power]/[water power]

BP or TP/WP

where:
BP = γQh*e_t
BP = 2πTN

Question 9

Electrical or Generator Efficiency, e_gen

Answer 9

[generator output]/Brake Power

where:
GP = TPe_gen = γQh (e_te_gen)

Question 10

Generator Speed, N

Answer 10

120f/P

f=frequency (usually 60hertz)
P = no. of poles (even number)

Question 11

Hydraulic Efficiency, e_h

Answer 11

h_w/h

h_w = utilized head
h = net head

Question 12

Head of Impulse turbine (PELTON), h

Answer 12

P/γ + V^2/2g

Question 13

Head of Reaction Turbine (FRANCIS AND KAPLAN), h

Answer 13

P/γ + z + (V_a^2 - V_b^2)/2g

Question 14

Peripheral Coefficiency, ⌀

Answer 14

Vp/Vj
πDN/[sqrt(2gh)]

Vp = peripheral velocity
Vj = velocity of jet
D = diameter of runner
N = angular speed
h = net head

Question 15

Specific Speed of Hydraulic Turbine, N_s

Answer 15

[N*sqrt(P)]/h^(5/4)

P = power
h = head in m or ft
N = speed in rpm

Question 16

total efficiency, e_total

Answer 16

e_total = e_h * e_m * e_v

e_h = hydraulic eff
e_m = mechanical efficiency
e_v = volumetric efficiency