Consider a horizontal 2 in. ×1 in. venturi with water flow. For a differential pressure of 25 ps

Consider a horizontal 2 in. ×1 in. venturi with water flow....

Key Concepts

Venturi Meter

A Venturi meter is a flow-measuring device that uses a constricted section (throat) in a pipe to create a pressure drop. This pressure drop is related to the fluid velocity through the constriction, allowing the flow rate to be calculated. The meter essentially applies the Venturi effect, where fluid speed increases as the flow area decreases, leading to a corresponding reduction in pressure.

Bernoulli's Principle

Bernoulli's principle states that for an incompressible, non-viscous fluid flowing in a streamline, the sum of its pressure energy, kinetic energy, and potential energy remains constant. This concept is used in the analysis of Venturi meters to relate the differences in pressure measured at different cross-sectional areas to the velocity of the fluid, thereby enabling flow rate calculations.

Continuity Equation

The continuity equation reflects the conservation of mass in fluid dynamics, stating that the product of cross-sectional area and fluid velocity is constant along a streamline for an incompressible fluid. In the context of a Venturi meter, this equation is used to correlate the velocities in the wider and narrower sections of the pipe, which is key to linking the measured differential pressure to the flow rate.

Differential Pressure Measurement

Differential pressure measurement involves recording the pressure drop between two points in a flow system. In the case of a Venturi meter, this pressure difference is directly linked to the change in fluid velocity as the fluid passes through varying areas. The measured differential pressure is a pivotal parameter for computing the volumetric flow rate using fluid dynamics equations.

Flow Rate Calculation and Unit Conversion

Flow rate calculation in fluid dynamics involves converting the measured pressure differential and corresponding velocities into a volumetric flow rate, often expressed in units like gallons per minute (gpm). This process includes applying the appropriate equations that relate pressure drop, fluid density, and cross-sectional area, along with necessary unit conversions to obtain the final flow rate in the desired units.

Transcript

00:01 Here let's calculate the ratio of throat diameter to pipe diameter that is beta veta will be equal to small d divided by capital d so it will be 1 divided by 2 that is equals to 0 .5 so now let reynolds number is greater than 2 multiplied by 10 to the power of 5 reference amount 2 multiplied by 10 to 4 5 so the range of coefficient of discharge so cofficent of discharge will vary from will vary in between in between 0 .98 is less than cd is less than 0 .995 let cd is equal to 0 .299.

01:04 Now let's calculate the volume flow rate.

01:10 Let's calculate the volume flow rate.

01:11 Q is equal to mass flow rate divided by row so it will be equal to cd a t divided by row root over 1 minus beta 2 the power of 4 multiplied by square root of 2 row del p so we will put it can further be reduced to equation of form pi d square multiplied by cd divided by square root of 4 multiplied by 1 minus beta 2 the power of 4 multiplied by square root of 2 del p divided by row hence from here we get volume flow rate is equal to pi 5 multiplied by 1 divided by 12 feet square multiplied by 0 .9 divided by divided by 4 multiplied by square root of 1 minus 0 .5 to the power of 4 multiplied by square root of square root of 2 multiplied by 36003600 .3600 .0193 lv per feet square divided by 1 .9 for sludge per feet so it will come out to be 0 .34 feet cube per second that will be equals to 152 152 gps gps now now the verification for the reynolds number so let's calculate the velocity is equal to discharge divided by area so it will be 4 q divided by pi d square pi d square so it will be 4 multiplied by q is equal to 0 .34 divided by pi multiplied with the diameter of the pipe is 2 inch is equal to 2 divided 12 feet so it will be equals to 15 .15 .57 feet per second feet per second so assuming the water in the pipe to be at temperature assume assume temperature is you assume temperature is equals to 68 degree fahrenheit so so the kinematic viscosity new will be equals to 1 .08 multiplied by 10 to the power of minus 5 pt square second pt square per second per second hence now we will calculate the reynolds number so reynolds number re will be equals to vd divided by new velocity is find velocity we have find as 15 .57 multiplied diameter is 2 inch 2 divided by 12 feet divided venue 1 .08 multiplied by 10 to the power of minus 5.

04:35 So from here we get reynolds number is equal to 2 .403 multiplied by 10 to the power of 5 which is greater than 2 multiplied by 10 to the power of 5...

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