A laboratory experiment is set up to measure pressure drop for flow of water through a smooth tu

A laboratory experiment is set up to measure pressure drop...

Key Concepts

Reynolds Number

The Reynolds number is a dimensionless parameter in fluid mechanics that indicates whether flow is laminar or turbulent. It is calculated based on fluid velocity, characteristic length (such as tube diameter), and fluid properties (density and viscosity). A high Reynolds number typically corresponds to turbulent flow, while a low Reynolds number indicates laminar flow.

Critical Reynolds Number

The critical Reynolds number represents the threshold value at which the flow transitions from laminar to turbulent. In many practical applications involving pipe flow, this value is around 2000 to 4000. Determining the critical Reynolds number is essential for predicting when turbulence will occur and hence for designing and analyzing fluid systems.

Volumetric Flow Rate

The volumetric flow rate is the volume of fluid that passes through a cross-section of a pipe per unit time. It is directly related to the fluid’s velocity and the cross-sectional area of the pipe. Calculating the required volumetric flow rate is important for ensuring that the flow conditions, such as achieving turbulent flow, are met in an experiment or application.

Head Loss (Pressure Drop)

Head loss, or pressure drop, refers to the loss of mechanical energy of the fluid due to friction and turbulence as it moves through a tube or pipe. The calculation of head loss often uses the Darcy-Weisbach equation, which incorporates factors such as flow velocity, pipe length, diameter, and friction factor. In experiments, measuring the reservoir height differential to overcome this head loss is critical for maintaining the desired flow regime.

Entrance Losses

Entrance losses occur due to the disturbance and additional energy dissipation as fluid enters a pipe, particularly when the entrance is sharp or square-edged. These losses affect the overall pressure drop and are important considerations when determining the necessary head difference to establish and sustain a turbulent flow regime in a tube.

Transcript

00:01 From continuity equation we can write the discharge q is equal to area multiplied by the velocity average velocity so we can write it as area multiplied by average velocity can be written as reynolds number multiplied by kinetic viscosity divided by diameter i will give you a brief reynolds number is equals to rho vd divided by mu or vd divided by new hence from here we get we get velocity v is equal to r e new divided by d so this we have put here in this equation so from this we get q is equal to pi d multiplied by renaud's number multiplied by aromatic viscosity divided by four divided or we can write for rhenolts number is equals to 2300 we can write for reynolds from a 2300 we can write discharge q is equal to pi multiplied by diameter is given as 15 .9 15 .9 mm which can be 15 .9 into 10 to minus 3 meter multiplied by reynolds from as 2300 multiplied by the kinematic viscosity of water at 20 degrees centigrade can be written as 1 .01 multiplied by 10 to the power of minus 6 this data is given is taken from the table provided in the book divided by 4 so from this we get the volume player rate q is equals to 2 .9 multiplied by 10 to the power of minus 2 .9 multiplied by 10 to the power of minus 5 meter cube per second so this is the required volume flow rate this is required volume flow rate now now let us write the head loss equation head loss equation head loss equation we can write p1 divided by row plus alpha 1 multiplied by v1 squared by 2 plus g z 1 minus p2 divided by row plus alpha 2 multiplied by r v2 squared by 2 plus gz2 is equals to frictional head loss plus minor head loss rate loss rate to this equation bickrition number 1 here hl frictional head loss is equal to flv squared divided by 2d and the minus head loss hlm is equal to k v squared divided by 2 now we assume assume p1 is equal to p2 is equal to p a tm is equal to 0 also v1 is equal to v2 is equal to 0 as from equation 1 from equation 1 we can write we can write z 1 minus z 2 is equal to v squared divided by 2g bracket close fl divided or d plus k let this is equation v equation v equation number 2 now again from continuity equation we can write velocity is equal to discharge divided by area so discharge is 2 .9 multiplied by 10 to the power of minus 3 area area is 5 divided by 4 multiplied by diameter square which is 15 .9 multiplied by 10 to the power of minus 3 whole square so after dividing we will get the velocity is 0 .146 meter per second now from figure now from figure friction factor for fully developed flow in circular pipe for turbulent flow in smooth pipe for turbulent flow in a smooth pipe in a smooth pipe we can write d is equal to z1 is equal to z2 and d will be equal to 0 .145 squared by 2g 2 multiplied by 9 .8 1 4 multiplied by 0 .05 multiplied by 3 .56 divided by 2 by 15 .9 multiplied by 10 to the power of minus 3 minus plus 0 .5 so from here we get d is equal to 0 .027 meter hence there is our wide differential height differential is 0 .027 so height is equal to 0 .0 27 meter.

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