V-Notch Weir Laboratory Experiment A

Background For V-Notch Weirs

Weirs

Use and Qualities •  Open Channel Flow Measurement

– A simple flow measurement tool – Details of design and calibration are documented

in many standards •  International Standards Organization •  ASTM International (American Society for Testing and

Materials) •  British Standards Institution •  United States Department of the Interior, Bureau of

Reclamation Water Measurement Manual •  etc.

V-Notch Design

V-Notch Design

Thick plate with exit chamfer Thin plate with no exit chamfer

Weir Features

D, the distance from the weir face to the point of head measurement H must be at least D = 4 HMAX (the maximum head height that can be measured by the weir). You may assume HMAX = A (top of concrete wall as shown on the next slide).The predicted flow rate is inaccurate when lower side of the stream wets the downstream chamfer-face. Standards may indicate the minimum as a fixed distance from the base of the V (sometimes called the crotch).

Weir Features

The design limits for a fully contracted v-notch weir are: H/P ≤ 0.4, H/C ≤ 0.2, P ≥ 0.45 m (1.5 ft), C≥ 0.9 m (3 ft) although others quote the following values: H/P ≤ 1.2, H/C ≤ 0.4, C ≥ 0.6 m, 0.60 ≥ H ≥ 0.05 m, P ≥ 0.10 m, minimum tailwater level ≥ 0.05 m, and 100°≥ 2α ≥ 25°

Weir Flow

Weir Experiment •  For a triangular weir with fluid height H,

the flow rate, Q is given by

•  Where

•  And C is an experimental discharge coefficient

•  This experiment is designed to find C.

5 28 2 tan15

Q C g H α= •

)/(tan 1 AB−=α

Venturi Laboratory Experiment B

Background For The Demonstration of Bernoulli’s Law

and the Continuity Equation

Fluid Pressure In A Venturi

Use and Qualities for Venturi •  Flow Monitoring and Pumping

– A simple flow measurement tool – Details of design and calibration are well

documented •  It is used where high pressure recovery is required

and mixing of gases. •  Can be used for measuring flow rates of water,

gases, suspended solids, slurries and dirty liquids. •  Can be used to measure high flow rates in pipes

having diameters of over a metre.

Venturi Features

Venturi Design •  The entry of the venturi is cylindrical in shape

to match the size of the pipe through which the fluid flows

•  The converging conical section has an included angle ( Angle 1) of 19º to 23º.

•  Following the converging section, there is a cylindrical section with the minimum area called the throat.

Venturi Design Continued •  Following the throat, there is a diverging

conical section with an included angle of 5º to 15º (Angle 2). This reduces friction losses, improving pressure recovery.

•  Openings at the entry and throat (at sections 1 and 2 in the diagram) of the venturi meter connection points for a differential pressure sensor (u-tube manometer, differential pressure gauge, etc.) as shown in diagram.

Venturi Advantages •  Less chance of getting clogged with sediment

when measuring flow. •  Its behaviour can be predicted easily

because the design is well documented. •  Can be installed vertically, horizontally or

inclined.

Venturi Disadvantages •  They can be large in size. This is a problem

where space is limited. •  Expensive initial cost, installation and

maintenance. •  Require long installation length. That is, the

venturi meter has to be proceeded by a straight pipe that is free from fittings and misalignments to avoid flow turbulence.

•  There is a lower limiting diameter; suggested to be 7.5 cm when used for measuring flow.

Venturi Experiment •  This experiment is designed to evaluate

the pressure recovery through a venturi meter by comparing the experimental pressure measurements, along its length, with the theoretically predicted from Bernoulli’s equation.

or

21 constant2

p V gzρ+ + =

2 21 1 ,1 12 2i i i Totalp V p V pρ ρ+ = + =

Bernoulli’s Equation Continued •  Where

– p is the fluid pressure – pi, Total is the total fluid pressure at the ith point – ρ is the density of the fluid – V is the fluid velocity – z is the elevation of the measurement point – g is the acceleration due to gravity – A is the cross-sectional area inside the venturi

Experimental Apparatus

Experiment Continued •  The difference between the experimental

venturi and the design presented above is that there are more static pressure taps in the diverging section and it is similar to the video.

•  A total pressure probe (measures static pressure of the fluid and the dynamic or velocity pressure of the fluid) can be positioned at each static pressure tap.

Experiment Continued •  The experiment is horizontal so there is no

elevation change and Bernoulli’s equation reduces to:

•  So, by comparing a reference point, 1, to the ith measurement point:

21 constant2

p Vρ+ =

2 21 1 ,1 12 2i i i Totalp V p V pρ ρ+ = + =

Experiment Continued •  The continuity equation is:

•  And, for the flow of water at STP, the density is assumed constant:

•  All that is needed is the measure the flow rate through the venturi and the rest is calculations.

1 1 1 i i iAV AVρ ρ=

1 1 i iAV AV=

Pipe Friction Laboratory Experiment C

Background For The Demonstration of Pipe Friction

Pipe Friction

In a horizontal pipeline flowing full, the head loss (hL) between any two points is given by:

1 2 and = gLp ph γ ργ−

=

Pipe Friction Continued •  Friction factor f, for flow of liquids fully

filling a pipeline is defined by:

•  The value of the friction factor is a function of the Reynolds Number (Re) and relative roughness (ε/D).

2

2

LhfL VD g

= Where L and D are the length and inside diameter of the pipe

Pipe Friction Continued •  Where

– p is the fluid pressure – hL is the head loss – γ is the specific weight of the fluid – ρ is the density of the fluid – V is the fluid velocity – D is the inside diameter of the pipe – L is the length of the pipe – g is the acceleration due to gravity

Pipe Friction Continued •  The following figure (Moody Diagram)

shows the functional dependence of f on Re and ε/D.

•  There are several important features of the Moody Diagram:

i.  For very smooth pipes and for laminar flow, f is a function of Re only, and

ii.  for wholly turbulent flow (as the Reynolds number becomes very high), f is a function of ε/D only.

Laboratory

The laboratory apparatus permits the measurement of head loss, hL and the volumetric rate of flow, Q. Along with the pipe geometry of diameter, D, and length, L, it provides sufficient information to calculate the friction factor for that pipe. The results can then be compared with the value from Moody’s diagram after calculating the Reynold’s number, Re.

Experimental Apparatus

Questions ??