HYDRAULICS

GENERAL PRINCIPLES

Hydraulics treats of liquids in motion, particularly of the flow of water through orifices, pipes, and channels.

The quantity of water, in cubic feet, flowing through a channel or a pipe in 1 sec. is called the discharge of the channel or the pipe in cubic feet per second and is denoted by Q. It is equal to the mean, or average, velocity of flow through the given section multiplied by its area, or

Q=vA,

in which v is the mean velocity, in feet per second, and A the area, in square feet. If the area of the channel or pipe varies, the mean velocities vary inversely as the corresponding cross

Aa, va and Ab, v¿ denoting, respectively, areas and corresponding velocities at two different cross-sections.

Hydrostatic Head and Pressure Head.-When water contained in any vessel or pipe discharges freely into the atmosphere, the velocity of discharge v, in feet per second, if frictional. and other resistances are neglected, is equal to

in which h is the vertical distance in feet of the point of discharge from the level of the water, and g=32.16. This velocity is produced by the pressure due to the weight of a column of water of the height h, the latter being called the static or hydrostatic head.

The water in the pipe or vessel may be subjected to an external pressure, thus giving an intensity of pressure greater than that due to the static head, or owing to losses during the flow, it may have an intensity of pressure which is smaller than that due to the static head. Let p be the intensity of pressure in pounds per square inch, and v' the velocity due to this pres sure; then,

W

in which w is the weight of a column of water 1 sq. in. in cross

section and 12 in. high, usually taken as .434 lb. The term

represents the head necessary to produce the pressure p and is called the pressure head.

The pressure head in a water pipe can be measured by the height to which the water will rise in a tube inserted in the pipe. Such a tube or gauge is called a piezometer or piezometric tube.

Velocity Head.-When water in a pipe or a channel is flowing to a level h ft. lower than the starting point, if frictional and other resistances are not considered, the velocity attained during the flow is v = √2 gh, which is the same as the velocity attained by a body falling through a height h. Solving for h,

Loss of Head.-Owing to frictional and other resistances, a loss of energy occurs in flowing water, thus reducing the theoretical velocity of the flow, and, consequently, the discharge. This loss is usually expressed as a fractional factor of the theo

Flow of Water Through a Standard Orifice.-When the water in flowing through a hole touches the opening on the inside edges only, the hole is a standard orifice.

=

The theoretical

in which A is the area of the orifice, and v √2gh, h being the head or the distance of the center of the orifice from the level surface of the water. The actual discharge is reduced on account of frictional resistances and contraction of the jet. The friction reduces the velocity to 98% of the theoretical velocity and the contraction reduces the cross-section of the issuing jet to 62% of the area of the orifice. The actual discharge is, therefore, Qa= .98X.62 Q=.61 A √2gh.