What you need to remember for midterm

viscosity units

kg / (m s)

viscosity for water

0.001002 kg / m s

omega units (angular velocity)

rad / s (T to the -1 power)

Torque units

(Kg x m²) / s^-2

one ft is how many meters

0.3048

1 inch is how many meters

0.0254

Energy equation

(P1/rho) +(V1)²/2g + Z1 + hA = (P2/rho) +(V2)²/2g + Z2 + hL

In energy equation, what is hA (h on the left hand side)?

head added to the fluid by pump

In energy equation, what is hL (h on the right hand side)?

head lost by fluid (major and minor losses)

W

relative discharge velocity

V

absolute discharge velocity

alpha angle

absolute flow angle

rpm to rad/s

omega = (2N(pi)) / 60

Blade speed

U = wr

Normal / radial component of absolute fluid velocity

Vn = Q / A

Tangential component of fluid velocity

Vt = U - Vncot(beta)

Power transferred to the fluid

W(dot) = m(dot)(U2Vt2 - U1Vt1)

Head developed by pump, knowing power

H = W(dot) / (rho)gQ

Head developed by pump, knowing power and mass flow rate

H = W(dot) / m(dot)g

Head developed by pump, not knowing power

H = (1/g)(U2Vt2 - U1Vt1)

Shutoff head

Ho = U2²/g

What is W?

Water relative to the blades, maybe. At least in question 10.3

Vt in terms of U and wt

VT = u - wt

Efficiency equation for a turbine

Eta = mechanical power / hydraulic power = bhp /((rho)gHQ

Specific Speed

Ωsp = (Ω((P/ρ)^1/2)) / ((gH)^5/4)

Pelton Wheel Jet Speed

Vj = sqrt(2gH)

Pelton wheel U

U = R(omega) = 0.47Vj

Pelton WHeel Diameter

D = 2U / omega

Pelton WHeel jet diameter

Q = VjAj = Vj(((pi)(dj)²)/4) → dj = sqrt((4Q/(pi)Vj))

Pelton WHeel Hydraulic power

W(dot)h = Tw = FU = FR(omega) = m(dot)U(1-cos(beta))(Vj - U)

Pelton Wheel Torque

W(dot)out = T x (omega) = T → W(dot)out / omega