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Discharge under Falling Head.

When the inflow is less than the outflow then that condition is called the falling head condition.The time required for a certain quantity of water to flow from a reservoir can be calculated by equating the volume of water that flows through the orifice or pipe in time dt to the volume decrease in the reservoir. If the area of the reservoir is constant,

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Flow Through Orifices.

Orifice Discharge into Free Air

An orifice is an opening with a closed perimeter through which water flows. Orifices may have any shape, although they are usually round, square, or rectangular.
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Pressure(head)Changes Caused By Pipe Size Change.

Energy losses occur in pipe contractions, bends, enlargements, and valves and other pipe fittings. These losses can usually be neglected if the length of the pipeline is greater than 1500 times the pipe diameter. However, in short pipe- lines, because these losses may exceed the friction losses, minor losses must be considered.
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Commonly Used Formula in Hydraulics

Darcy Weisbach formula
Darcy Weisbach formula which is valid for laminar or turbulent flow in all fluids is one of the most commonly used formula for determining the head loss.

hf=[fLV2]/2gD

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Fluid flow in pipes

Laminar Flow

Its is a flow in which the fluid particles move in parallel layers in a single direction.Due to the parabolic velocity distribution in laminar flow, a shearing stress is developed. As this shearing stress increases, the viscous forces become unable to damp out disturbances, and turbulent flow results. The region of change is dependent on the fluid velocity, density, and viscosity and the size of the conduit.

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