Weirs and Notches MCQ Quiz - Objective Question with Answer for Weirs and Notches - Download Free PDF

Explanation:

• In a trapezoidal weir, the sides are inclined outward to provide structural stability and help manage flow efficiently.

• According to standard hydraulic design practices, the slope of the sides is generally taken as 1 vertical to 4 horizontal (1:4).

• This slope ensures proper flow distribution and ease of construction.

Additional Information

• A trapezoidal weir is a hydraulic structure used to measure flow in open channels and rivers. 

• It has a trapezoidal cross-section with the sides inclined outward, usually at a slope of 1 vertical to 4 horizontal.

• The trapezoidal shape helps to control the flow smoothly and reduces turbulence compared to sharp-edged weirs.

• It is commonly used for larger flow measurements because the shape allows handling a wide range of flow rates efficiently.

• The discharge over the weir is calculated using standard empirical formulas that consider the shape and dimensions.

• Trapezoidal weirs are easier to construct and maintain compared to rectangular or triangular weirs, making them practical for many irrigation and drainage applications.

Explanation:

The discharge (Q) through a rectangular notch in an open channel flow is given by the formula:

Q=CLH^3/2

Where:

• Q is the discharge (flow rate),

• C is a constant depending on the shape of the notch,

• L is the length (width) of the notch,

• H is the head (the height of water above the bottom of the notch).

From this formula, you can see that discharge Q is directly proportional to the width (L) of the notch. This means that if the width of the notch is doubled, the discharge will double as well, assuming the head (H) remains the same.

 Additional Information

Effect of Changing the Width (L):

1. The discharge is directly proportional to the width (L) of the rectangular notch. This means that if the width is doubled, the discharge will double, as long as the head (H) remains constant.

Discharge Coefficient (C):

1. The discharge coefficient C depends on factors like the shape of the notch, the flow type (subcritical or supercritical), and the specific characteristics of the flow.

2. For a sharp-crested weir (a type of notch), C is a constant that generally depends on experimental results, and it can be adjusted based on the characteristics of the flow and the notch.

Concept:

The discharge through a Crump’s open flume outlet is given by:

\( Q = C \cdot L_t \cdot H^{3/2} \)

• \( C = 1.60 \)
• \( L_t = 7 \, \text{cm} = 0.07 \, \text{m} \)
• \( H = 0.64 \, \text{m} \)

Substituting values:

\( Q = 1.60 \cdot 0.07 \cdot (0.64)^{3/2} \approx 0.0573 \, \text{cumecs} \)

Explanation:

Types of Weirs

Weirs are categorized based on several criteria:

1. Types of Weirs based on Shape of the Opening

• Rectangular weir

• Triangular weir

• Trapezoidal weir

Rectangular Weir:

• A standard weir shape suitable for larger flowing channels.

• To calculate discharge, the flow over the rectangular weir is analyzed by considering an elementary horizontal strip of water, and the total discharge is determined through integration.

Triangular Weir:

• Also known as a V-notch weir, with a reverse triangle shape.

• Ideal for measuring discharge over small flows with greater accuracy.

• Discharge calculation involves considering an elementary horizontal strip and integrating to determine the total discharge.

Trapezoidal Weir:

• Also called Cipoletti weir, a modification of the rectangular weir with a trapezoidal shape.

• Suitable for slightly higher capacity for the same crest strength.

• Total discharge over the trapezoidal weir is calculated by combining the discharge over rectangular and triangular weirs.

Additional InformationTypes of Weirs based on Shape of the Crest

• Sharp-crested weir
• Broad-crested weir
• Narrow-crested weir
• Ogee-shaped weir

Explanation:

A triangular notch (V-notch) is a type of flow measuring device used to measure low discharges in open channels. It has the following advantages:

1. Higher Sensitivity for Low Discharges:

   • The V-notch provides more accurate readings for small discharge rates because even minor changes in flow depth cause significant changes in discharge.

   • This makes it highly sensitive for measuring low flows.

2. Self-Cleansing Effect:

   • The sharp V-shape helps in preventing debris accumulation and ensures a free flow of water.

Explanation:

1) Sutro or Proportional  weir:

2) Parshall flume

3) Weir and notch

Concept:

Cippoletti weir

• The Cippoletti weir is a trapezoidal weir, having side slopes 1 horizontal to 4 vertical.
• The purpose of the slope, on the sides, is to obtain an increased discharge through the triangular portions of the weir, which otherwise would have been decreased due to end contractions in the case of rectangular weirs.
• A type of contracted weir that is related to the rectangular sharp-crested weir is Cippoletti weir, which has a trapezoidal cross-section with side slopes 1: 4 (H: V).

Explanation:

Weir or notch is a physical structure of masonry constructed across the channel width to calculate the discharge of the channel section.

Rectangular Notch:

The discharge through a rectangular notch weir is,

\(Q = \frac{2}{3}{C_d}L\;\sqrt {2g} \;{H^{3/2}}\)

Where, Q = discharge of fluid, Cd = Coefficient of discharge and H = height of water above the notch

Triangular Notch:

A V-notch weir is also called the triangular notch or weir. The discharge over a triangular weir or notch is given by the:

\(Q = \frac{8}{{15}}{C_d}tan\frac{\theta }{2}\;\sqrt {2g} \;{H^{5/2}}\)

Where, Q = discharge of fluid, Cd = Coefficient of discharge, θ = Notch angle and H = height of water above the notch

Trapezoidal weir (or) Notch:

\(Q = \frac{2}{3}{C_{{d_1}}}\sqrt {2g} \;LH^{\frac{3}{2}} + \frac{8}{{15}}{C_{{d_2}}}\sqrt {2g} .\tan \frac{\theta }{2}.{H^{\frac{5}{2}}}\)

Where, \(\left( {\frac{\theta }{2}} \right)\) = weir angle of inclination with the vertical.

\({C_{{d_1}}}\) = Coefficient of discharge for rectangular portion.

\({C_{{d_2}}}\) = Coefficient of discharge for the triangular portion.

Answer:

Statement 4: False Ventilation of triangular weir is not necessary.

Weir:

A weir is a concrete or masonary structure, placed in an open channel over which the flow occurs. It is generally in the form of vertical wall, with a sharp edge at the top, running all the way across the open channel. The notch is of small size while the weir is of a bigger size. The notch is generally made of metallic plate while weir is made of concrete or masonary structure.

Triangular weir:

The expression for the discharge over a triangular weir or notch is

Q = \(\frac{8}{{15}} \times {C_d} \times tan\frac{θ }{2} \times \sqrt {2g} \times {H^{\frac{5}{2}}}\)

From this expression flow through the weir depend upon the vertex angle (θ) and coefficient of discharge (C_d) is constant for all the heads, the value of C_d is nearly equal to 0.6.

Rectangular weir:

The expression for the discharge over a rectangular weir or notch is

Q = \(\frac{2}{3} \times {C_d}\; \times L \times \sqrt {2g} \times {H^{\frac{3}{2}}}\)

Advantage of triangular weir over rectangular weir:

A triangular weir is preferred to a rectangular weir due to following reason.

(1) The expression for discharge for a right angled V- notch or weir is very simple.

(2) For measuring low discharge, a triangular weir gives more accurate results than a rectangular weir.

(3) In case of triangular weir, only one reading, (H) is required for the computation of discharge.

(4) Ventilation of triangular weir is not necessary.

Explanation:

Weir or notch is a physical structure of masonry constructed across the channel width to calculate the discharge of the channel section.

Rectangular Notch:

The discharge through a rectangular notch weir is,

\(Q = \frac{2}{3}{C_d}L\;\sqrt {2g} \;{H^{3/2}}\)

Where, Q = discharge of fluid, Cd = Coefficient of discharge, and H = height of water above the notch

Triangular Notch:

A V-notch weir is also called the triangular notch or weir. The discharge over a triangular weir or notch is given by the:

\(Q = \frac{8}{{15}}{C_d}tan\frac{\theta }{2}\;\sqrt {2g} \;{H^{5/2}}\)

Where, Q = discharge of fluid, Cd = Coefficient of discharge, θ = Notch angle, and H = height of water above the notch

A triangular notch or weir is preferred to a rectangular weir or notch due to the following reasons:

• The expression for discharge for a right-angled V-notch or weir is very simple.
• For measuring the low discharge, a triangular notch gives more accurate results than a rectangular.
• In the case of the triangular notch, only one reading i.e H is required for the computation of discharge.

Concept:

Cipolletti weir is a trapezoidal weir having 1H: 4V side slope.

Discharge of Cipoletti weir Q = 1.84 × L × H^3/2

where, L = Length of the weir, H = Head over the weir

Calculation:

Given:

L = 200 cm = 2 m, H = 100 cm = 1 m

Discharge of Cipoletti weir Q = 1.84 × L × H3/2 = 1.84 × 2 × 1^3/2 = 3.68 m³/sec

Explanation:

For a given value of specific energy, the critical depth gives the greatest discharge, or conversely, for a given discharge, the specific energy is a minimum for the critical depth.

For rectangular channels, the critical depth,

dc(m), is given by

\({d_c} = {\left[ {\frac{{{Q^2}}}{{{b^2}g}}} \right]^{\frac{1}{3}}} \)

Where dc = critical depth (in m), Q = quantity of flow or discharge (in m3/s), B = Width of channel (in m)

Explanation:

Submerged weir:

• When the water level on the downstream side of a weir is above the crest of the weir, then the weir is called to be a submerged or downed weir.
• The total discharge, over the weir, is obtained by dividing the weir into two parts.
• The portion between upstream and downstream water surface may be treated as a free weir and the portion between downstream water surface and crest of the weir as a drowned weir.

• The thin jet of water passing through the weir opening is called the nappe.
• There should always be air under the nappe of a sharp-crested weir otherwise negative pressure will be created which may damage the weir structure on the downstream side.
• An arrangement for aeration under the nappe is necessary when the weir used is suppressed rectangular weir. This may require the installation of an air vent pipe through the sidewall of the channel to provide air under the nappe. If the nappe is not aerated, the weir will deliver more flow than that actual flow.
• Therefore, in order to maintain constant discharge, aeration is a must.

Classification of weir based on shape of crest:

1. Sharp crested weir: The crest shape of the weir is very sharp. It is most widely used weir.

2. Broad-crested weir: These are constructed only in a rectangular shape and are suitable for the larger flows.

3. Narrow-crested weir: It is similar to rectangular weir with a narrow shaped crest at the top. The discharge over the narrow crested weir is similar to discharge over the rectangular weir.

4. Ogee-shaped weir: Generally ogee shaped weirs are provided for the spillway of a storage dam. The crest of the ogee weir is slightly risen and falls into parabolic form.

Explanation: