Abstract
A new idea is introduced to explain the mechanism of drag reduction in turbulent pipe flow of dilute polymer solutions.
Assume that there is a stress relaxation phenomenon for a polymer in solution and define a new quantity known as the dynamic viscosity. Also assume that the viscosity of a Newtonian fluid is the sum of the laminar and turbulent viscosities where the turbulent viscosity is defined under the assumption that the product of the friction factor and Reynolds number has the value 16 for any Reynolds number. In the case of polymer solutions, further add the dynamic viscosity to the sum of the laminar and turbulent viscosities and assume that the same relation between friction factor and Reynolds number may be established.
From these considerations the ratio of the friction factor of a polymer solution to that of a Newtonian fluid can be related to the concentration of polymer solution, molecular weight, pipe diameter and Reynolds number as variables. Good agreement is obtained and theoretical considerations are verified by experiment. The friction factor of CMC solution in turbulent flow can be estimated when concentration of polymer solution, molecular weight, pipe diameter and Reynolds number are given.
