ME-313, IIT Gandhinagar, Dept. of Mechanical Engineering Page 1 Frictional Losses in Circular Pipes Aim To observe the dependency between Reynolds number and friction factor for flow of water through circular pipes in turbulent flow regime and compare it with theoretical predictions. To use Moody Charts to determine the surface roughness factor of the internal walls of circular pipes. Apparatus Four test sections, made-up of circular pipes of different diameters, each with two pressure tapings on upstream and downstream side. Differential pressure cell for measuring frictional pressure drop across given test section. Water circulation system consisting of water reservoir, a centrifugal pump with a bypass line for changing the flow rate of water through test section. A digital flow meter for measuring the flow rate of water through the test section. Theory Changes to inviscid, incompressible flow from point a to point b is given by Bernoulli’s equation. = + () 2 2Bernoulli's equation states that the total head h along a streamline remains constant. This means that velocity head can be converted into gravity head and/or pressure head or vice- versa, such that the total head h stays constant implying that no energy is lost for such a flow. This situation corresponds to ideal fluid flow. However for real viscous fluids, frictional losses due to the viscous boundary layer along the pipe walls leads to head loss along the length of the pipe in the direction of the flow. Therefore one cannot use Bernoulli's principle of conserved head (or energy) to calculate flow parameters. However one could still keep track of this head loss by incorporating another term called viscous head into Bernoulli's equation. As the flow moves along the pipe, viscous head accumulates gradually taking available head away from the pressure, gravity, and velocity heads. However the conservation of energy implies that the total head h (or energy) remains constant. If the pipe diameter D remains constant along the length L of the pipe (as is the case with the current experiment) then by
Transcript
ME-313, IIT Gandhinagar, Dept. of Mechanical Engineering Page 1
Frictional Losses in Circular Pipes
Aim
To observe the dependency between Reynolds number and friction factor for flow of water through circular pipes in turbulent flow regime and compare it with theoretical predictions.
To use Moody Charts to determine the surface roughness factor of the internal walls of circular pipes.
Apparatus
Four test sections, made-up of circular pipes of different diameters, each with two pressure tapings on upstream and downstream side.
Differential pressure cell for measuring frictional pressure drop across given test section.
Water circulation system consisting of water reservoir, a centrifugal pump with a bypass line for changing the flow rate of water through test section.
A digital flow meter for measuring the flow rate of water through the test section.
Theory
Changes to inviscid, incompressible flow from point a to point b is given by Bernoulli’s equation.
=𝑝 𝑥
𝜌𝑔+
𝑈(𝑥)2
2𝑔
Bernoulli's equation states that the total head h along a streamline remains constant.
This means that velocity head can be converted into gravity head and/or pressure head or vice-versa, such that the total head h stays constant implying that no energy is lost for such a flow. This situation corresponds to ideal fluid flow. However for real viscous fluids, frictional losses due to the viscous boundary layer along the pipe walls leads to head loss along the length of the pipe in the direction of the flow.
Therefore one cannot use Bernoulli's principle of conserved head (or energy) to calculate flow parameters. However one could still keep track of this head loss by incorporating another term called viscous head into Bernoulli's equation.
As the flow moves along the pipe, viscous head accumulates gradually taking available head away from the pressure, gravity, and velocity heads. However the conservation of energy implies that the total head h (or energy) remains constant. If the pipe diameter D remains constant along the length L of the pipe (as is the case with the current experiment) then by
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conservation of mass between any two stations (continuity equation), the fluid velocity U remains constant along the pipe. The Darcy-Weisbach Equation enables the estimation of experimental value of the pipe friction factor.
𝑓 =2 𝑝𝐴 − 𝑝𝐵 𝐷𝑔
𝜌𝑢2𝐿
In general, f depends on the Reynolds Number Re of the pipe flow and the relative roughness of the pipe wall. The function needs to be determined by theory or experiment. The roughness measure Σ is the average size of the bumps on the pipe wall. The relative roughness Σ/D corresponds to statistical measure of the size of the surface asperities which arise from pipe manufacturing and surface finish processes compared with the diameter of the pipe. For commercial pipes this is usually a very small number and perfectly smooth pipes should have a roughness of zero.
For laminar flow (Re < 2000 in pipes), f can be deduced analytically by comparing the pressure change between points A and B defined by Eqn. (3) with the pressure drop corresponding to the Hagen-Poiseuille Equation which defines the pressure drop of incompressible laminar viscous flow in a long circular pipe.
This leads the Fanning’s friction factor (mainly used by Chemical Engineers) for laminar flow in circular pipes as follows
Fanning f =16/Re
The Darcy friction factor or Moody’s friction factor (mainly used by Mechanical and Civil
Engineers) is four times the magnitude of Fanning’s friction factor, i.e.
Darcy f =64/Re
The difference arises because of the use of hydraulic diameter in the Darcy–Weisbach
formula instead of the pipe diameter in Fanning’s formula. The hydraulic radius calculation involves dividing the cross sectional area of flow by the wetted perimeter. For a round pipe with full flow the hydraulic radius is equal to ¼ of the pipe diameter.
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Moody Charts often indicate the type of friction factor, or at least provide the formula for the friction factor with laminar flow. If the formula for laminar flow is f = 16/Re, it's the Fanning factor, and if the formula for laminar flow is f = 64/Re, it's the Darcy–Weisbach factor.
Procedure
Fill the reservoir with water to about 90% of its capacity.
Select the test section by opening the ball valve leading to that test section keeping the ball valve leading to other test section closed.
Open the valve on the suction side of the pump. Open the valve on the bypass line of the pump fully.
Switch on the power supply of the pump.
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Adjust the desired flow rate of water through the test section by manipulating the valve on the test section as well as the valve on the bypass line of the pump.
Note down the pressure differential across the test section making use of differential pressure cell.
Read the flow rate from the given flow meter.
Take last reading at the maximum possible flow rate through the test section.
Record the following parameters: Inside diameter of pipe (D) Distance between two pressure tapings (L) Average temperature of water during the run Density, Dynamic , Kinematic Viscosity of water at average temperature
Data Average temperature=300 C Density=995.7 kg/m3 Kinematic viscosity=0.805x 10-6 Distance between two pressure tapings (L) = 1 m
Observation
Diameter(mm) ΔP(kPa) Flow(lit/min)
pipe 1 10.7 10 2.6
pipe 2 23.6 3.9 4.1
pipe 3 7.3 17.7 4.3
pipe 4 4.5 103.2 4
Calculation
Velocity Re Friction factor f(Darcy friction factor)
pipe 1 0.482153013 6408.742 3.281750035 0.009986
pipe 2 0.15629279 4582 2.822918442 0.013968
pipe 3 1.713175394 15535.63 3.962943197 0.00412
pipe 4 4.193861236 23443.94 14.24340857 0.00273
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Graph
Conclusion The relation between Reynolds’s number and friction factor was studied and was found to be decreasing with increase in Reynold’s number.
