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Water wheel

Updated: Wikipedia source

Water wheel

A water wheel is a machine for converting the kinetic energy of flowing or falling water into useful forms of power, often in a watermill. A water wheel consists of a large wheel (usually constructed from wood or metal), with numerous blades or buckets attached to the outer rim forming the drive mechanism. Water wheels were still in commercial use well into the 20th century, although they are no longer in common use today. Water wheels are used for milling flour in gristmills, grinding wood into pulp for papermaking, hammering wrought iron, machining, ore crushing and pounding fibre for use in the manufacture of cloth. Some water wheels are fed by water from a mill pond, which is formed when a flowing stream is dammed. A channel for the water flowing to or from a water wheel is called a mill race. The race bringing water from the mill pond to the water wheel is a headrace; the one carrying water after it has left the wheel is commonly referred to as a tailrace. Waterwheels were used for various purposes from things such as agriculture to metallurgy in ancient civilizations spanning the Near East, Hellenistic world, China, Roman Empire and India. Waterwheels saw continued use in the post-classical age, like in medieval Europe and the Islamic Golden Age, but also elsewhere. In the mid- to late 18th century John Smeaton's scientific investigation of the water wheel led to significant increases in efficiency, supplying much-needed power for the Industrial Revolution. Water wheels began being displaced by the smaller, less expensive and more efficient turbine, developed by Benoît Fourneyron, beginning with his first model in 1827. Turbines are capable of handling high heads, or elevations, that exceed the capability of practical-sized waterwheels. The main difficulty of water wheels is their dependence on flowing water, which limits where they can be located. Modern hydroelectric dams can be viewed as the descendants of the water wheel, as they too take advantage of the movement of water downhill.

Tables

· Types › Summary of types
Stream (also known as free surface). Ship wheels are a type of stream wheel. Vertical wheel with horizontal axle The bottom of the wheel is placed into flowing water Driving surfaces – blades – flat prior to 18th century, curved thereafter Water – very large volume, no head Efficiency – about 20% prior to 18th century and later 50 to 60%
Stream (also known as free surface). Ship wheels are a type of stream wheel. Vertical wheel with horizontal axle The bottom of the wheel is placed into flowing water Driving surfaces – blades – flat prior to 18th century, curved thereafter Water – very large volume, no head Efficiency – about 20% prior to 18th century and later 50 to 60%
Col 2
Undershot Vertical wheel with horizontal axle The water hits the wheel low down, typically in the bottom quarter Driving surfaces – blades – flat prior to 18th century, curved thereafter Water – large volume, low head Efficiency – about 20% prior to 18th century and later 50 to 60%
Undershot Vertical wheel with horizontal axle The water hits the wheel low down, typically in the bottom quarter Driving surfaces – blades – flat prior to 18th century, curved thereafter Water – large volume, low head Efficiency – about 20% prior to 18th century and later 50 to 60%
Col 2
Breastshot Vertical wheel with horizontal axle The water hits the wheel roughly central, typically between one quarter and three quarters of the height. Driving surfaces – buckets – carefully shaped to ensure that the water enters smoothly Water – large volume, moderate head Efficiency – 50 to 60%
Breastshot Vertical wheel with horizontal axle The water hits the wheel roughly central, typically between one quarter and three quarters of the height. Driving surfaces – buckets – carefully shaped to ensure that the water enters smoothly Water – large volume, moderate head Efficiency – 50 to 60%
Col 2
Overshot Vertical wheel with horizontal axle The water hits near the top of the wheel and in front of the axle so that it turns away from the head race Driving surfaces – buckets Water – low volume, large head Efficiency – 80 to 90%
Overshot Vertical wheel with horizontal axle The water hits near the top of the wheel and in front of the axle so that it turns away from the head race Driving surfaces – buckets Water – low volume, large head Efficiency – 80 to 90%
Col 2
Backshot (also known as pitchback) Vertical wheel with horizontal axle The water hits near the top of the wheel and before the axle so that it turns back towards the head race Driving surfaces – buckets Water – low volume, large head Efficiency – 80 to 90%
Backshot (also known as pitchback) Vertical wheel with horizontal axle The water hits near the top of the wheel and before the axle so that it turns back towards the head race Driving surfaces – buckets Water – low volume, large head Efficiency – 80 to 90%
Col 2
Vertical axis also known as tub or Norse mills. Horizontal wheel with a vertical axis A jet of water strikes blades mounted on the axle Driving surfaces – blades Water – low volume, high head Efficiency – poor
Stream (also known as free surface). Ship wheels are a type of stream wheel. Vertical wheel with horizontal axle The bottom of the wheel is placed into flowing water Driving surfaces – blades – flat prior to 18th century, curved thereafter Water – very large volume, no head Efficiency – about 20% prior to 18th century and later 50 to 60%
Undershot Vertical wheel with horizontal axle The water hits the wheel low down, typically in the bottom quarter Driving surfaces – blades – flat prior to 18th century, curved thereafter Water – large volume, low head Efficiency – about 20% prior to 18th century and later 50 to 60%
Breastshot Vertical wheel with horizontal axle The water hits the wheel roughly central, typically between one quarter and three quarters of the height. Driving surfaces – buckets – carefully shaped to ensure that the water enters smoothly Water – large volume, moderate head Efficiency – 50 to 60%
Overshot Vertical wheel with horizontal axle The water hits near the top of the wheel and in front of the axle so that it turns away from the head race Driving surfaces – buckets Water – low volume, large head Efficiency – 80 to 90%
Backshot (also known as pitchback) Vertical wheel with horizontal axle The water hits near the top of the wheel and before the axle so that it turns back towards the head race Driving surfaces – buckets Water – low volume, large head Efficiency – 80 to 90%
· The power of a wheel › Formulae
Power
Power
Quantity
Power
Formula
P = η ⋅ ρ ⋅ g ⋅ h ⋅ q ˙ {\displaystyle P=\eta \cdot \rho \cdot g\cdot h\cdot {\dot {q}}}
Effective head
Effective head
Quantity
Effective head
Formula
h = h p + h v {\displaystyle h=h_{p}+h_{v}}
Velocity head
Velocity head
Quantity
Velocity head
Formula
h v = v 2 2 ⋅ g {\displaystyle h_{v}={\frac {v^{2}}{2\cdot g}}}
Volume flow rate
Volume flow rate
Quantity
Volume flow rate
Formula
q ˙ = A ⋅ v {\displaystyle {\dot {q}}=A\cdot v}
Water velocity (speed)
Water velocity (speed)
Quantity
Water velocity (speed)
Formula
v = k ⋅ d t {\displaystyle v=k\cdot {\frac {d}{t}}}
Quantity
Formula
Power
P = η ⋅ ρ ⋅ g ⋅ h ⋅ q ˙ {\displaystyle P=\eta \cdot ho \cdot g\cdot h\cdot {\dot {q}}}
Effective head
h = +h_{v}}
Velocity head
h v = v 2 2 ⋅ ={\frac {v^{2}}{2\cdot g}}}
Volume flow rate
q ˙ = A ⋅ }=A\cdot v}
Water velocity (speed)
v = k ⋅ {t}}}
· The power of a wheel › Rules of thumb › Breast and overshot
Power (assuming 70% efficiency)
Power (assuming 70% efficiency)
Quantity
Power (assuming 70% efficiency)
Approximate formula
P = 7000 ⋅ q ˙ ⋅ h {\displaystyle P=7000\cdot {\dot {q}}\cdot h}
Optimal rotational speed
Optimal rotational speed
Quantity
Optimal rotational speed
Approximate formula
21 D {\displaystyle {\frac {21}{\sqrt {D}}}} rpm
Quantity
Approximate formula
Power (assuming 70% efficiency)
P = 7000 ⋅ q ˙ ⋅ }\cdot h}
Optimal rotational speed
21 {\sqrt {D}}}} rpm
· The power of a wheel › Rules of thumb › Traditional undershot wheels
Power (assuming 20% efficiency)
Power (assuming 20% efficiency)
Quantity
Power (assuming 20% efficiency)
Approximate formula
P = 100 ⋅ A ⋅ v 3 {\displaystyle P=100\cdot A\cdot v^{3}}
Optimal rotational speed
Optimal rotational speed
Quantity
Optimal rotational speed
Approximate formula
9 ⋅ v D {\displaystyle {\frac {9\cdot v}{D}}} rpm
Quantity
Approximate formula
Power (assuming 20% efficiency)
P = 100 ⋅ A ⋅ }
Optimal rotational speed
9 ⋅ {D}}} rpm

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