Water at 65^∘ C flows through a 75 -mm-diameter orifice installed in a 150 -mm-i.d. pipe. The fl

Water at 65^∘ C flows through a 75 -mm-diameter orifice...

Key Concepts

Fluid Properties (Temperature Effects)

Fluid properties, such as density and viscosity, can be influenced by temperature changes. In practical flow measurements, knowing the temperature-dependent properties is crucial, as these factors affect the flow behavior and the resulting pressure drop across measurement devices like orifice plates.

Pressure Differential Measurement

Pressure differential measurement refers to the technique of measuring the difference in pressure across a device, such as an orifice plate, to infer properties of the flow. In many flow measurement systems, pressure taps are strategically placed to capture this differential, which is then used to evaluate the flow rate based on established fluid dynamics principles.

Discharge Coefficient

The discharge coefficient is a corrective factor applied in orifice flow calculations to account for non-idealities such as energy losses, viscosity, and flow separation. It adjusts the theoretical flow rate derived from the ideal energy conservation equations to align more closely with empirical observations.

Bernoulli’s Principle

Bernoulli’s Principle explains the conservation of energy in fluid flow. It states that an increase in the speed of the fluid occurs simultaneously with a decrease in pressure or potential energy along a streamline. This concept is fundamental in analyzing how velocity changes across a constriction, like an orifice, lead to measurable pressure differences.

Orifice Meter Equation

The orifice meter equation is used to relate the pressure drop across an orifice to the flow rate through it. It stems from applying the conservation of energy (Bernoulli’s Principle) and accounts for the geometry of the orifice and the pipe. This equation is pivotal in translating differential pressure readings into flow rate measurements.

Transcript

00:01 The mass flow rate equation for a flow meter can be written as m actual m actual is equal k -80 root over 2 row multiplied by p -1 minus p -2 p -2.

00:20 Now from here we get del p -p which is equal to p -1 minus p -2 is equal to m dot divided by k -at k -kat whole square whole square multiplied by 1 by 2 row.

00:35 Let this equation be equation 1.

00:37 Also from continuity equation from continuity equation we can write v is equal to q divided by area or q is given as 20 liter per second so it will be 20 multiplied by 10 to per minus 3 meter q per second divided by area is pi divided or 4 multiplied by d square so diameter is given as 75 which is equal to 75 multiplied by 10 to the power of minus 3 meter so it will be square i divided 4d square so this will come out to be this will come out to be here the diameter of the id pipe is 150 so let's put it 150 not not 75 so let's put it 150 it will be 150 150 150 square so it will come out to be 1 .13 meter per second meter per second now, reynolds number can be written as re.

01:38 Ree is equal to velocity multiplied by diameter divided kinematic viscosity.

01:43 Now, we will put the velocity as 1 .13 multiplied where diameter is given as 150 mm, which is equal to 150 multiplied by 1020 .000 per of minus 3 meter.

01:55 Aided electromagnetic viscosity can be gained from the table from the table of property of water at temperature 65.

02:03 It will be 4 .4 multiplied by 10 to the power of minus 7 meter square per second so after calculation we get r e is equal to 3 .85 multiplied by 10 to the power of 5 so this is the rennals number now the diameter ratio dia ratio can be written as can be written as beta which is equal to d t divided by d1 d1 so this is equal to dt is 75 where d1 is 150.

02:40 It will be 0 .5.

02:43 Now from the figure flow coefficient of concentric orifice with corner tap for r .e...

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