Calculate the volumetric flow rate by dividing the volume by the time of collection:𝑉̇=𝑉/𝑡.

Laminar and Turbulent Pipe Flow3

Remember to examine the flow to see if you can establish when the flow is laminar, transitional and turbulent. Hint: carefully examine the way the dye behaves when it is in the tube at the different flow rates.

Take sketches (or digital photos) of the different dye behaviour with steadily increasing flow of the dyeProcedureWe use a narrow bore tube, which has a largelength to diameter ratio.

Water flows through the tube from a constant head device and the flow rate is controlled by a valve. The pressure loss is measured using water manometers (for low flow rates) or mercury manometers for the higher flow rates.

Record a schematic diagram of the equipment.

Make a note of the pipe diameter and the length of the pipe between the pressure tappings.

Open the control valve until a difference of about 5 cm appears on the water manometer.

Note the actual difference in levels and collect aknown quantity of water in a known time (at least 30 seconds), to get the flow rate.

Ensure that the quantity of water measured is enough to be measured accurately and to reduce the possibility of error.

Ensure the minimum water collection time is 30 seconds

Repeat the procedure increasing the head loss in 5 cm steps until the limit of the water/air manometer is reached.

Transfer to the water/mercury manometer and take readings in about 2cm steps until the limit of the flow is reached.

Ensure that you measure the temperature of the water for each test, since the viscosity is a function of temperature.Analysis of Results

For each of the mercury manometer readings, convert the head loss in cm of mercury to head loss in cm of water by multiplying by 12.6.

Calculate the volumetric flow rate by dividing the volume by the time of collection:𝑉̇=𝑉/𝑡.Note: be careful with units (1m3= 1000 litres and 1 litre = 1000ml)

Calculate the average velocity: 𝑢=4𝑉̇/𝜋𝑑2.

Calculate the Reynolds number: Re=𝜌𝑢𝑑/𝜇.

Calculate the friction factor three different ways:

1.Solve the Darcy equation for friction factor 𝑓and use your data to evaluate the value at each point.

2.Use the Blasius equation.

3.Use the Moody diagram.

Presentation of ResultsPlot a graph of head loss incm of water ℎ𝑓against volumetric flow rate𝑉̇.

Draw the Poiseuille equation on the graph.

Discussion

The laminar region can be identified by the points that agree with the Poiseuille equation.