Join Sarthaks eConnect Today - Largest Online Education Community!
0 votes
10 views
asked in Physics by (28.3k points)

A tube of length l and radius R carries a steady flow of fluid whose density is ρ and viscosity η.The velocity v of flow is given by

V = V0 ( 1 -r2/R2),

where r is the distance of flowing fluid from the axis. Find

(a) Volume of fluid, flowing across the section of the tube, in unit time. 

(b) Kinetic energy of the fluid within the volume of the tube 

(c) The frictional force exerted on the tube by the fluid, and 

(d) The difference of pressures at the ends of the tube.

1 Answer

+1 vote
answered by (24.7k points)
selected by
 
Best answer

(a) Let us consider a cylindrical section at a distance of r and having thickness dr. 

The volume of fluid flowing from this section per second

So, the volume of fluid flowing across the section of the tube in unit time

(b) The kinetic energy of the fluid within the volume element of thickness dr 

So, the K.E. of fluid within the tube

Integrating, we get

(c) The viscous drag exerts a force on the tube

(d) The pressure difference ΔP is given by

ΔP = P2 – P1 = P

Where P1 = 0 & P2 = P

As we know that

P = Force (F)/ area of section of tube

Related questions

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

One Thought Forever

“There is a close connection between getting up in the world and getting up in the morning.“
– Anon
~~~*****~~~

Categories

...