# Measuring viscosity of water through use of Poiseuille equation

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Abstract

The purpose of this experiment was to determine the viscosity of water using Poiseuille’s equation. The results obtained indicated that rate of flow of water was directly proportional to the height of water in the tube.

Introduction

Viscosity is a property of a fluid that demonstrates the fluid’s resistance to flow. Viscosity in liquids occurs because of the cohesive forces between different molecules as they move past each other. There are various factors that affect how fast a fluid flows through a pipe. These factors are summarized by Poiseuille equation, as shown in Equation 1 below:

……………………………………….. (1)

Where  = volume flow rate, ρ = density of fluid, g = gravitational acceleration, h = height of fluid in pipe, a = radius of pipe, L = length of pipe, and ɳ = viscosity of fluid.

This experiment involved determining the viscosity of water using Poiseuille equation. Three different types of tubes were used (with different lengths (L) and radii (a)).

Method

A ruler was used to measure the lengths (L) of the tubes and a traveling microscope was used to measure the radii (a) of the tubes. A wrench was used to attach the black tube to a large tank. Water was filled in the tank to a known height (h). Water was released from the tank to flow through a tube into a beaker that was placed on an electric beaker, for a period of 60 seconds. The mass of the water in the beaker was measured and recorded. After recording the mass, the water in the beaker was returned into the tank. This process was repeated four more times so as to get recordings of 5 masses of water.

Results

The data obtained from the experiment was as shown in Table 1 below:

 Height (cm) Mass in 60s (g) Average mass in 60s (g) Error in mass (g) Rate cm3/s Error on rate #1 #2 #3 #4 #5 1.0 7.6 7.8 7.4 7.3 7.2 7.46 0.107703296 0.124333333 0.002854957 2.0 12.9 12.9 12.9 12.7 12.6 12.8 0.063245553 0.213333333 0.002855668 3.0 17.3 16.8 16.6 15.8 15 16.3 0.404969135 0.271666667 0.009089117 4.0 21.8 23.2 22.5 21.8 22.5 22.36 0.261916017 0.372666667 0.007533603 5.0 25.2 24 22.3 21.6 20.8 22.78 0.80274529 0.379666667 0.016681994

Table 1: Experimental data

Figure 1: Graph showing rate, cm3/s against height, cm

Discussion

The results, as indicated in Figure 1 above, shows that the rate of flow of water through the pipe was directly proportional to the height of the water. From the chi square analysis of the results, the difference between observed and expected results was insignificance.

References

1. Dolz, M.J. Hernandez, J. Delegido and A. Casanovas. A laboratory experiment on inferring Poiseuille’s law for undergraduate students. European Journal of Physics, 27 (2006) 1083-1089: Institute of Physics Publishing.

University of Delaware. Experiment 8: size of a molecule from a viscosity measurement. University of Delaware, 2014.

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