0

Guest

Courses New

A dimensionally consistent relation for the volume V of a liquid of coefficient of viscosity ( η ) flowing per second through a tube of radius (r) & lenght (l) & having a pressure (P) across its end is a. V = π pr 4 / 8 ηl b. V = π ηl / 8pr 4 c. V = 8p ηl / π r 4 d. V = π p η / 8lr 4

 

A dimensionally consistent relation for the volume V of a liquid of coefficient of viscosity (η) flowing per second through a tube of radius (r) & lenght (l) & having a pressure (P) across its end is

a.  V = π pr4 / 8ηl

b. V =  π ηl / 8pr4

c. V = 8pηl / π r4 

d. V = π pη / 8lr4

Grade:12th pass

4 Answers

Santosh Datla
askIITians Faculty 77 Points
7 years ago
524-569_Sol.JPG
Aditya
13 Points
5 years ago
In the above all options , according to the question , n ,v ,p and l should be there , and in the above mentioned options in only 1 all are present so a is the correct answer
Kushagra Madhukar
askIITians Faculty 628 Points
3 years ago
Hello student.
As given the unknown dimensional variables are p, r, l, η 
p = [ML-1T-2]
r = [L1]
l = [L1]
η = F.r/A.v = (ML1T-2)(L)/(L2)(LT-1) = [ML-1T-1]
The dimension of Volume flow per second, V = [L3T-1]
 
Now, we can solve this by taking the power of each dimensional variable as unknowns and then solving four linear equations to obtain the correct relationship conventionally.
But, since it is an MCQ with available options it is better to use option approach. 
 
Now, we see in option (a)
LHS = V = [L3T-1]
RHS =  π pr4 / 8ηl = (ML-1T-2)(L4) / (ML-1T-1)(L)
                              = [L3T-1]
                              = LHS
Hence, option (a) is correct
 
Hope it helps
Regards,
Kushagra
Kushagra Madhukar
askIITians Faculty 628 Points
3 years ago
Dear student,
Please find the attached solution to your question.
 
As given the unknown dimensional variables are p, r, l, η 
p = [ML-1T-2]
r = [L1]
l = [L1]
η = F.r/A.v = (ML1T-2)(L)/(L2)(LT-1) = [ML-1T-1]
The dimension of Volume flow per second, V = [L3T-1]
 
Now, we can solve this by taking the power of each dimensional variable as unknowns and then solving four linear equations to obtain the correct relationship conventionally.
But, since it is an MCQ with available options it is better to use option approach. 
 
Now, we see in option (a)
LHS = V = [L3T-1]
RHS =  π pr4 / 8ηl = (ML-1T-2)(L4) / (ML-1T-1)(L)
                              = [L3T-1]
                              = LHS
Hence, option (a) is correct
 
Hope this helps.
Thanks and regards,
Kushagra

Think You Can Provide A Better Answer ?

Other Related Questions on Mechanics

View all Questions »

ASK QUESTION

Get your questions answered by the expert for free

Answer and earn gift vouchers

Win Gift vouchers upto Rs 500/-

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More