Objective

To verify the law of the resistance of a system of ducts connected in series.

Apparatus used:

Pitot Tube, Inclined U-Tube Manometer, Flexible Rubber Tubes, Ventilation Duct etc.

Description Resistance in Series: If two or more airways are connected in series then each of those sets of resistance may be combined into a single equivalent resistance. It allows considerable simplification of the schematic representation of actual subsurface ventilation systems.

STEP  1 

Start the motor to allow the fan to attain the constant 300 rpm.

The knob is being rotated

The Motor reading = 300 rpm

STEP  2 

Calculating the angle of inclination of inclined U-Tube Manometer.

↑

tan θ = h/l

θ = tan^-1(h/l)

θ = (θ₁+θ₂+θ₃)/3 = 7.74°

Point No

Length(l)(cm)

Height(h)(cm)

Angle(θ°)

STEP  4 

Connect flexible rubber tube of manometer to Pitot Tube fixed at point 1 of ventilation duct.

Note:

1.The Pitot Tube should be fixed at point 1 in the ventilation duct tightly.
2.Connect one flexible rubber tube of manometer with Total Head of Pitot Tube to take the reading of static pressure.
3.Remove rubber tube from Total Head and connect that with Static Head of Pitot Tube to take the reading of total pressure.
4.Now, connect one flexible rubber tube of manometer with Total Head and another with Static Head of Pitot Tube to take the reading of velocity pressure.

   

Isometric View of the Ventilation Duct

Top View of the inclined U-Tube Manometer

Point 1

Total Head

Pitot Tube

Static Head

First flexible rubber tube is connected to the Static Head

Second flexible rubber tube is connected to the Total Head

Both flexible rubber tubes are connected to the Static Head and Total Head

R₁

R₂

R₃

R₄

Observations:

Variables in calculation θ :Angle of inclination of the manometer tube = 7.74°

ρ :Specific gravity of the manometer liquid = 0.789

g :Acceleration due to gravity = 9.8 ms^-2

q :Density of air = 1.2 kg/m³

L_s1 :Length of static head at point 1

L_t1 :Length of total head at point 1

L_v1 :Length of velocity head at point 1

D :The diameter of the ventilation duct = 0.45 m

π = 3.14

	Static Head(cm)			Total Head(cm)			Velocity Head(cm)
No	Left Limb Reading	Right Limb Reading	Diffe rence (Ls1)	Left Limb Reading	Right Limb Reading	Diffe rence (Lt1)	Left Limb Reading	Right Limb Reading	Diffe rence (Lv1)
1

STEP  5 

Connect flexible rubber tube of manometer to Pitot Tube fixed at point 2 of ventilation duct.

Top View of the inclined U-Tube Manometer

Point 2

Observations:

Variables in calculation θ :Angle of inclination of the manometer tube = 7.74°

ρ :Specific gravity of the manometer liquid = 0.789

g :Acceleration due to gravity = 9.8 ms^-2

q :Density of air = 1.2 kg/m³

V₁ :Velocity of air at point 1 = m/s

L_s2 :Length of Static Head at point 2

L_t2 :Length of Total Head at point 2

L_v2 :Length of Velocity Head at point 2

	Static Head(cm)			Total Head(cm)			Velocity Head(cm)
No	Left Limb Reading	Right Limb Reading	Diffe rence (Ls2)	Left Limb Reading	Right Limb Reading	Diffe rence (Lt2)	Left Limb Reading	Right Limb Reading	Diffe rence (Lv2)
2

Observations:

Variables in calculation P_t1 :Total Head pressure at point 1 = Pa

P_t2 :Total Head pressure at point 2 = Pa

A :Area of cross section = 0.159

V₂ :Velocity of air at point 2 = m/s

Q₁ :Quantity of air passing through the ventilation duct at point 1 (Q₁) = m/s

Repeat the same procedure to calculate the resistance R₂₃, R₃₄ and R₁₄.

Result:

The law of resistance of a system of ducts connected in series is verified.