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Hydraulics

Forces Due To Pipe Bends

The momentum change and the unbalanced internal pressure of the water leads to forces on the pipes
The force diagram in figure is a convenient method for finding the resultant force on a bend. The forces can be resolved into X and Y components to find the magnitude and direction of the resultant force on the pipe.
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Temperature Expansion Of Pipe

If a pipe is subject to a wide range of temperatures, the stress, lb/in2 (MPa), due to a temperature change is
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Pipe Stresses Perpendicular To The Longitudinal Axis

The internal or external pressures on the pipe walls cause the stresses acting perpendicular to the longitudinal axis of a pipe. Internal pressure creates a stress commonly called hoop tension

The sum of the forces in the horizontal direction is

pD=2F

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Water Hammer

Water hammer is a change in pressure, either above or below the normal pressure, caused by a variation of the flow rate in a pipe.

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Orifice Discharge Into Diverging Conical Tubes

This type of tube can greatly increase the flow through an orifice by reducing the pressure at the orifice below atmospheric. The formula that follows for the pressure at the entrance to the tube is obtained by writing the Bernoulli equation for points 1 and 3 and points 1 and 2

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Fluid Jets

Where the effect of air resistance is small, the path of projectile is followed when a fluid discharged through an orifice into the air
The initial velocity of the jet is

V0 = Cv?2gh

where h= head on center line of orifice, ft (m),
Cv =coefficient of velocity.

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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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