Fluid mechanics


by: ranjan317
Fluid mechanics is the branch of physics that studies fluids (liquids, gases, and plasmas) and the forces on them. Fluid mechanics can be divided into fluid statics, the study of fluids at rest; fluid kinematics, the study of fluids in motion; and fluid dynamics, the study of the effect of forces on fluid motion. It is a branch of continuum mechanics, a subject which models matter without using the information that it is made out of atoms, that is, it models matter from a macroscopic viewpoint rather than from a microscopic viewpoint.



IWeirs and notches
 

Weir Definition

A structure, used to dam up a stream or river, over which the water flows, is called a weir. The conditions of flow, in the case of a weir, are practically the same as those of a rectangular notch. That is why, a notch is, sometimes, called as a weir and vice versa.

The only difference between a notch and a weir is that the notch of a small size and the weir is of a bigger one. Moreover, a notch is usually made in a plate, whereas a notch is made of masonry or concrete.

Types Of Weirs

There are many types of weirs depending upon their shape, nature of discharge, width of crest and nature of crest. But the following are important from the subject point of view :

1. According to the shape :
  • Rectangular weir
  • Cippoletti weir

2. According to the nature of discharge :
  • Ordinary weir
  • Submerged or drowned weir

3. According to the width of crest :
  • Narrow crested weir
  • Broad crested weir

4. According to the nature of crest :
  • Sharp crested weir
  • Ogee weir

Velocity Of Approach

Sometimes, a weir is provided in a stream or a river to measure the flow of water. In such a case, the water, approaching the weir, has got some velocity, known as velocity of approach. It is assumed to be uniform over the whole weir.Let,

  • A = Cross sectional area of the channel on the upstream side of the weir, and
  • Q = Discharge over the weir

\therefore Velocity of approach,
v = \frac{Q}{A}

Notch

A notch may be defined as an opening in one side of a tank or a reservoir, like a large orifice, with the upstream liquid level below the top edge of the opening.
23547/notch.png
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Since the top edge of the notch above the liquid level serves no purpose, therefore a notch may have only the bottom edge and sides.

The bottom edge, over which the liquid flows, is known as sill or crest of the notch and the sheet of liquid flowing over a notch (or a weir) is known as nappe or vein. A notch is, usually made of a metallic plate and is used to measure the discharge of liquids.

Types Of Notches

There are many types of notches, depending upon their shapes. But the following are important from the subject point of view.

  • Rectangular notch
  • Triangular notch
  • Trapezoidal notch
  • Stepped notch
 
IICalculation of discharge over a rectangular notch (or weir)

Calculation of discharge over a rectangular notch (or weir)
IIICalculation of length of a rectangular notch (or weir)

Calculation of length of a rectangular notch (or weir)
IVCalculation of discharge over a triangular notch or weir

Calculation of discharge over a triangular notch or weir
VCalculation of discharge through a trapezoidal notch

Calculation of discharge through a trapezoidal notch
VICalculation of discharge through a stepped notch

Calculation of discharge through a stepped notch
VIITime required to lower water to a particular level by rectangular notch

Time required to lower water to a particular level by rectangular notch (or) Level to which water falls in a given time
VIIITime required to lower water to a particular level by triangular notch

Time required to lower water to a particular level by triangular notch
IXCalculation of discharge over a rectangular weir considering velocity of approach

Calculation of discharge over a rectangular weir considering velocity of approach
XCalculation of discharge over Cipolletti weir or notch

Calculation of discharge over Cipolletti weir or notch
XICalculation of discharge over a broad-crested weir or notch

Calculation of discharge over a broad-crested weir or notch
XIICalculation of discharge over a narrow-crested weir or notch

Calculation of discharge over a narrow-crested weir or notch