Hydraulics Lab: Head Loss in Pipes with Equations | CE251

Hydraulics Lab: Head Loss in Pipes

Lab Information

Lab No.: 2 – Head Loss in Pipes

Course Code: CE251 – Hydraulics

Description: Complete lab material covering Head Loss in Pipes experiment including theory, calculations, Darcy-Weisbach equation and lab report format

Credit: Important Notes

Head Loss in Pipes

Lab No. 2

Lab Syllabus: Head Loss in Pipes

Lab 2: Head Loss in Pipes Experiment

• Theory of fluid friction and head loss in pipes

• Darcy-Weisbach equation and friction factor

• Reynolds number and flow regimes

• Experimental setup and procedure for head loss measurement

• Calculation of friction factor and comparison with theoretical values

• Analysis of head loss vs. velocity relationship

Lab Report Content

Experiment: Head Loss in Pipe Experiment

Objective

To study the head loss due to friction in a straight circular pipe and verify the results using the Darcy-Weisbach equation. The experiment also explores the effect of varying flow rates on head loss, velocity, Reynolds number, and friction factor.

Apparatus Required

Horizontal pipe setup (2 m length, 1.905 cm diameter)
Inverted U-tube manometer (water used as manometric fluid)
Stopwatch
Thermometer
Measuring cylinder/discharge tank
Manifold with pressure tapping points
Flow control valve and rotameter

Scope

Head loss in pipelines directly affects the efficiency and energy consumption in water transport systems, industrial pipelines, and irrigation schemes. Understanding the frictional loss behavior under various flow conditions helps optimize designs and reduce power costs in fluid systems.

Theory

When water flows through a pipe, friction between the fluid and pipe wall causes a pressure drop known as head loss (hf). The Darcy-Weisbach equation is widely used to quantify this:

h_f = f \cdot \frac{L}{D} \cdot \frac{V^2}{2g}

Where:

\( h_f \): head loss (m)
\( f \): friction factor (dimensionless)
\( L \): pipe length (2 m)
\( D \): pipe diameter (0.01905 m)
\( V \): velocity of water (m/s)
\( g \): acceleration due to gravity (9.81 m/s²)

Reynolds Number:

Re = \frac{VD}{\nu}

Where \( \nu \) is the kinematic viscosity of water. At 29°C, dynamic viscosity \( \mu = 0.001 \, \text{Pa·s} \) and \( \nu = \mu/\rho = 1 \times 10^{-6} \, \text{m}^2/\text{s} \).

Flow is:

Laminar if \( Re < 2000 \)
Turbulent if \( Re > 4000 \)

For turbulent flow in smooth pipes, friction factor can be estimated using the Swamee-Jain equation:

\frac{1}{\sqrt{f}} = 1.74 – 2 \log_{10} \left( \frac{e}{D} + \frac{18.7}{Re \sqrt{f}} \right)

Where:

\( e \): pipe roughness (0.00005 m)

Procedure

The apparatus was set up and the pump was started.
A pipe of known diameter (1.905 cm) was selected, and valves were adjusted to allow flow.
Manometer cocks were opened, ensuring water filled both limbs completely.
Pressure tappings were connected and air was removed.
The flow rate was adjusted using the control valve.
Manometer readings \( h_1 \) and \( h_2 \) were taken to determine head loss.
Discharge was measured using a cylinder and stopwatch.
Steps 2–7 were repeated for multiple flow rates.
Water temperature was noted to calculate viscosity.

Observation Table

Length of pipe (L): 2 m
Diameter of pipe (D): 1.905 cm = 0.01905 m
Temperature: 29°C
Dynamic viscosity \( \mu \): 0.001 Pa·s
Roughness \( e \): 0.00005 m

S.N.	Discharge (Q) (L/hr)	Head Loss \( h_f \) (mm)
1	300	27.5
2	500	35.0
3	600	50.0
4	700	54.0
5	800	71.0
6	900	90.0
7	1000	108.0

Calculation Table

S.N.	Q (m³/s)	\( h_f \) (m)	V (m/s)	\( V^2/2g \)	\( h_f/(V^2/2g) \)	Re	f (exp)	f (theory)
1	8.33×10⁻⁵	0.0275	0.232	0.00274	10.04	5562.6	0.33	≈ 0.032
2	1.389×10⁻⁴	0.035	0.387	0.00763	4.59	10277.85	0.035	≈ 0.031
3	1.667×10⁻⁴	0.050	0.585	0.01745	2.86	11444.25	0.033	≈ 0.030
4	1.944×10⁻⁴	0.054	0.682	0.0237	2.28	13001.65	0.032	≈ 0.030
5	2.222×10⁻⁴	0.071	0.780	0.031	2.29	14855.0	0.032	≈ 0.030
6	2.5×10⁻⁴	0.090	0.877	0.039	2.31	16706.85	0.031	≈ 0.030
7	2.77×10⁻⁴	0.108	0.972	0.048	2.25	18516.6	0.031	≈ 0.030

Sample Calculations (S.N. 1)

Discharge:

Q = \frac{300}{3600} = 8.33 \times 10^{-5} \, \text{m}^3/\text{s}

Area:

A = \frac{\pi d^2}{4} = \frac{\pi (0.01905)^2}{4} = 2.85 \times 10^{-4} \, \text{m}^2

Velocity:

V = \frac{Q}{A} = \frac{8.33 \times 10^{-5}}{2.85 \times 10^{-4}} = 0.232 \, \text{m/s}

Head Loss:

h_f = \frac{27.5}{1000} = 0.0275 \, \text{m}

Reynolds Number:

Re = \frac{VD}{\nu} = \frac{0.232 \times 0.01905}{1 \times 10^{-6}} = 5562.6

Friction Factor:

f = \frac{h_f \cdot D \cdot 2g}{LV^2} = 0.33

Results

The friction factor decreased slightly with increasing Reynolds number, consistent with turbulent flow.
Experimental friction factors were close to theoretical values.
The relationship between head loss and flow velocity was confirmed.

Conclusion

The experiment successfully demonstrated how head loss increases with velocity and varies with pipe diameter and flow regime. The Darcy-Weisbach equation proved valid for estimating head losses in straight pipes. The experimental friction factors aligned well with theoretical predictions, validating the analytical approach.

Precautions

Ensured no air bubbles were trapped in the manometer.
Steady flow was ensured before recording readings.
Pipe fittings were checked for leaks.
Stopwatch readings were taken precisely for accurate discharge calculation.
High-sensitivity manometer was used for small head losses.

Lab Material (Important Notes)

Prepared by: Important Notes