Measurement of Velocity Profile in a Square Duct

ME 400

Jafar Samarah

Motasem Abu Shanap

Aim of the experiments is to obtain the velocity profile in square duct at different location along x-axis.

Velocity Profile Measuring Devices. Pressure Measuring Devices. Pitot Static Tube. Pressure Transducers.

Introduction

Viscous flow Laminar, Transition and Turbulent flow Reynolds Number Hydraulic diameter Entrance length

Principles

Viscosity is a measure of the resistance of a fluid which is being deformed by shear stress.

Dynamic viscosity. Kinematic viscosity .

Viscous Flow

Laminar Flow, Re<2300. Transition Flow, 2300<Re<4000. Turbulent Flow, Re>4000.

Flow Regimes

Re= Re = It is a dominant factor to specify the flow

regimes.

Reynolds Number

= , where: A= cross section area. Ρ= wetted perimeter.

Hydraulic Diameter

It is the length required to reach the fully developed flow.

Entrance Length

Conservation of Mass Conservation of Momentum Navier stokes equation Euler's Equation Bernoulli's equation

Governing Equations

=+

ρ1A1V1=ρ2A2V2, for Steady flow

Conservation of Mass

ρ(+u++w)= - + μ ( ++ +ρgx

: is the unsteady term. u++w :is the convective terms. :is the pressure Gradient (in x-direction). ++ :is the diffusion term.

Navier Stokes Equation

It is valid for inviscid flow where μ=0. ρ(+u++w)= - +ρgx

Euler's Equation

derived from Euler’s Equation, for a flow in a stream line. Fluid particles are subject only to pressure and their own weight.

P + ρV2 +gρz = Constant

Bernoulli's Equation

Square Cross Section (20X20cm) and 2 m long duct.

Fan. Glass piece on the side of the duct. Nozzle. Pitot Static Device. Signal Reading Device with Pressure

Transducers. Straighteners.

Experimental Setup

Experimental Setup

Experimental Results

We Obtained The Velocity Profiles at The Locations Shown in The Figures

Figure 4.3 shows the velocity profile for the duct channel along x-axis with variation of y-axis, without straws at fixed z=0 cm. For each location we took 5 readings of velocity, and then we

took the average velocity ⊽.

0 5 10 15 20 250

1

2

3

4

5

6

7

8

200cm,Vm=5.479m/s190cm,Vm=5.333m/s160cm,Vm=5.454m/s140cm,Vm=5.529m/s

⊽[m/s]

y-axis (cm)

In figure 4.4, velocity profile Over y-Axis With Fixed Height z=0 cm, along x-Axis without straws. Normalized by dividing each

velocity by the mean one, ⊽/Vm.

0 0.2 0.4 0.6 0.8 1 1.20

0.2

0.4

0.6

0.8

1

1.2

1.4

200cm,Vm=5.479m/s190cm,Vm=5.333m/s160cm,Vm=5.453m/s140cm,Vm=5.529m/s

⊽/𝑉_𝑚

𝑑𝑦/(𝑑𝑦_𝑚𝑎𝑥 )

Figure 4.5 shows the velocity profile for the duct channel along x-axis with variation of z-axis, without straws and fixed height

y=0cm.For each location we took 5 readings of velocity, and then we

took the average ⊽.

0 5 10 15 20 250

1

2

3

4

5

6

7

8

x=160cm,Vm=5.514 m/sx=180cm,Vm=5.433m/sx=200cm,Vm=5.533m/s

⊽[m/s]

z-axis (cm)

Figure 4.6 shows the velocity profile for the duct channel along x-axis with variation of z-axis, without straws and fixed height

y=0cm. it is normalized by dividing the velocity of each location by the mean velocity ⊽/Vm.

0 0.2 0.4 0.6 0.8 1 1.20

0.2

0.4

0.6

0.8

1

1.2

1.4

x =160cm,Vm=5.513m/sx=180cm,Vm=5.433m/sx=200cm,Vm=5.533m/s

⊽/𝑉_𝑚

𝑑𝑧/(𝑑𝑧_𝑚𝑎𝑥 )

Figure 4.7,Comparing the results at x=180 cm, for y & z axis

0 5 10 15 20 250

1

2

3

4

5

6

7

8

x=180cm, z axisx=180cm,y axis

z axis (cm)y axis (cm)

⊽[m/s]

Vibration of the duct due to the fan rotation. Irregularity of the duct shape. Extra friction due to the flange connection. Eccentricity of the fan eye. Vibration of Pitot static tube due to the air

flow. The Frame of the glass which gives extra

friction.

Conclusion

?Questions