Calculate the viscosity of a fluid to determine how well it resists flowing. Viscosity is commonly measured in units of Poise. The larger a fluids viscosity the more difficult it is for it to flow. For example, the viscosity of blood measures about 0.04 Poise while heavy oil has a viscosity of 6.6 Poise. Poiseuille's Law stares that the viscosity of a fluid flowing in a pipe depends on its volume flow rate, the difference in pressure at the pipe's ends, the pipe length and the pipe radius. Radius measures the distance from the centre of the pipe's circular side to its edge.
- Skill level:
- Moderately Challenging
Things you need
Subtract the value of the lower pressure end of the pipe from the value of the higher pressure end to get the difference. Use units of pascals. For example, the pressure difference might be 100 pascals.
Multiply the number pi times the pressure difference times the radius of the pipe, in meters, raised to the fourth power. Use 3.14 for pi, and call this result "X." Assuming the pipe radius to be 0.10m (about 4 inches), you have 3.14 times 100 pascal times 0.10m times 0.10m times 0.10m times 0.10m, or 0.031 pascal times meter^4 for "X." The symbol "^" denotes an exponent and is read as "to the power."
Multiply 8 times the volume flow rate, in meters per second, times the length of the pipe in meters. Call this result "Y." Assume the volume flow rate to be 1/2 gallon, or 0.0019 cubic meters, per second and the pipe length to be 2.5m. Continuing the exercise, you have 8 times 0.0019 cubic meters per second times 2.5m, or 0.038 meter^4 per second.
Divide "X" by "Y" to obtain the viscosity of the fluid in units of pascal times second. This step yields 0.031 pascal times meter^4 divided by 0.038 meter^4 per second, or a viscosity of 0.82 pascal times second.
Convert the viscosity to Poise by multiplying by 10, since 10 pascal times second equals a Poise. Completing the exercise leads to 0.82 pascal times second times 10 Poise per pascal times second, or a viscosity of 8.2 Poise. This viscosity is greater than heavy oil.
Tips and warnings
- Use metric units when calculating viscosity to obtain correct results.
- Volume flow rate measures the volume of a fluid passing a given point divided by the time that passes.
- Pressure measures the force per unit area applied to a surface.
- One pound per square inch (psi) equals 6,894.8 pascal.
- One meter equals 39.37 inches.
- One cubic meter equals 264.2 gallons.
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