Flow Through Notches

Flow Through Notches Points : Flow Through Notches, Types of Notches, Discharge over a Rectangular Notch, Discharge. over a Triangular Notch, Advantages of a Triangular Notch over a Rectangular Notch, Discharge over a Trapezoidal Notch, Discharge over a stepped notch, Discharge over the trapezoidal notch Notches A notch may be defined as an opening in one side of a tank or a reservoirs like large orifice, with the upstream liquid level below the top edge of the opening as shown in figure. Since the top edge of the notch above the liquid kel serves i.e. purpose, therefore a notch may have only the bottom edge 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 liquid.

Types of Notches There are many types of notche, depending upon their shapes But the following are important from the subject point of view:
1. Rectangular notch,
2. Triangular notch,
3 Trapezoidal notch, and
4. Stepped notch,
In this chapter, we shall discuss the discharge or the phenomenon associated with discharge over all these notches one by-one. Discharge over a Rectangular Notch Consider a rectangular notch in one side of a tank over which water is flowing as shown in figure.
Let H = Height of water above sill of the notch.
b = Width or length of the notch, and C
C¬₂ = Coefficient of discharge.

Fig. 11-2: Rectangular notch. Let us consider a horizontal strip of water of thickness dh at a depth of h from the water level as shown.
Area of the strip = b.dh
We know that the theoretical velocity of water through the strip

Note: Sometimes, the limits of integration, in the above equation, are from //, to H² (i.e.. the liquid level is at a height of//, above the top of the notch and H₂ above the bottom of the notch, instead of 0 to 1/. Then the discharge over such a notch will be given by the equation:

Discharge over a Triangular Notch A triangular notch is also called a i-notch. Consider a triangular notch, in one sideof the tank, over which water is flowing as shown
Let H = Height of the liquid above
the apex of the not
? Angle of the notch, and
C_d = Coefficient of discharge. From the geometry of the figure, we find that the width of the notch at the water surface

Advantages of a Triangular Notch over a Rectangular Notch 1. Only one reading I.E., head (H) is required to be taken for the measurement of discharge in a given triangular notch.
2. If in a triangular notch the angle of the notch i.e.. 0 = 90°, the formula becomes very simple (I.E., Q = 1.417 IP) to remember.
3. A traingular notch gives more accurate results for low discharges than a rectangular notch.
4. The same triangular notch can measure a wide range of flows accurately. Discharge over a Trapezoidal Notch A trapezoidal notch is a combination of a rectangular notch and two triangular notches as shown. It is, thus, obvious that the discharge over such a notch will be the sum of the discharges over the rectangular and triangular notches.

Consider a trapezoidal notch ABCD as shown in Fig. For analysis purpose, split up the into a rectangular notch BCFE and two triangular notches ABE and DCF. The discharge over a single two triangular notches is equivalent to the discharge over a single triangular notch of angle O

Let
H = Height of the liquid above the sill of the notch
C_dl Coefficient of discharge for the rectangular portion,
C_d2 = Coefficient of discharge for the triangular portions,
b = Breach h of the rectangular portion of the
q/2 = Angle, which the sides make with the vertical

Discharge over the trapezoidal notch
Q Discharge over the rectangular notch
+Discharge over the triangular notch.

Discharge over a stepped notch A Stepped notch is a combination of rectangular notches as shown is thus obvious that the discharge over such a notch will be sum of discharges over the different rectangular notches.

Consider a stepped notch as shown in fig analysis pill pose, let into two rectangular notches 1 and 2. The tor discharge over the notch will discharges over the two rectangular notches.

Let
H₁ = Height of the liquid above sill of notch I.
b₂ = Breadth of notch I.
H₂ b₂ Corresponding values for notch 2. and
C_d = Coefficient of discharge A-r both the notch-I
From the geometry of the notch, we find that the discharge over the note –1