Two liquids of densities and are flowing in identical capillary tubes under the same pressure difference. If and are the time taken for the flow of equal quantities (Mass) of liquids. What will be the ratio of the coefficient of viscosity of liquids?
Step 1: Given parameters
Two liquids have different densities and at time and respectively.
Step 2: Formula used
According to Poiseuille’s equation, the volume() of liquid flowing per second (say ) in a capillary tube, is given by
.
Where, is the time, is the length of the pipe, is the dynamic viscosity, is the pressure difference between the two ends, and, is the radius of the pipe
Now mass () is and density () related to volume as , so equation (1) can be written as.
Now for each liquid,
Step 3: Calculate the ratio of the coefficient of viscosity of liquids
Using and dividing (2) by (3), we get
Hence, the ratio .