wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Two liquids of densities D1 and D2 are flowing in identical capillary tubes under the same pressure difference. If T1 and T2 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?


Open in App
Solution

Step 1: Given parameters

Two liquids have different densities D1 and D2 at time T1 and T2 respectively.

Step 2: Formula used

According to Poiseuille’s equation, the volume(V) of liquid flowing per second (say T) in a capillary tube, is given by

Q=VT=πr4∆P8ηL......(1).

Where, T is the time, Lis the length of the pipe, η is the dynamic viscosity, ∆P is the pressure difference between the two ends, and, r is the radius of the pipe

Now mass (m) is and density (D) related to volume as V=mD, so equation (1) can be written as.

Qm=mT=πr4∆P8ηLD

Now for each liquid,

m1T1=πr4∆P8η1LD1.......(2)m2T2=πr4∆P8η2LD2........(3)

Step 3: Calculate the ratio of the coefficient of viscosity of liquids

Using m1=m2 and dividing (2) by (3), we get

⇒T2T1=D1D2×η2η1⇒η1η2=D1T1D2T2

Hence, the ratio η1:η2=D1T1:D2T2.


flag
Suggest Corrections
thumbs-up
2
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Viscosity
PHYSICS
Watch in App
Join BYJU'S Learning Program
CrossIcon