A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 one year ago
ques
anonymous
 one year ago
ques

This Question is Closed

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1440220440808:dw This is a volume element of in an imcompressible fluid flowing at a distance x,y,z from the respective axes In the book it is given coordinates of P as x,y,z but shouldn't they be (x+dx),(y+dy),(z+dz) or (dx),(dy),(dz) if we consider the element at origin Let \[\vec V=V_{x}\hat i+V_{y}\hat j+V_{z}\hat k\] be the velocity of fluid at a point P(x,y,z) Mass of fluid flowing through face ABCD in unit time is \[=V_{x}(dy.dz)\] Now the problem is right in starting, this equation is dimensionally incorrect, the left side is having a unit of mass but right side is jut made up of velocity and length elements

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Maybe what they mean by P(x,y,z) is \[\vec V \equiv \vec V(x,y,z)\] A vector point function \[\vec V=V_{x}(x,y,z)\hat i+V_{y}(x,y,z)\hat j+V_{z}(x,y,z)\hat k\] But using a notation like this makes u think the coordinates of P are x,y,z but that's impossible if the length is dx,dy,dz how can it have coordinates x,y,z It must have either (dx,dy,0) or (x+dx,y+dy,0) Depending on where we taking our volume element (point P lies in the xy plane, so z=0)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@ganeshie8 @IrishBoy123

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.1In the Gospel of Mary, V is defined as \(\vec V = \rho \vec v\) with units \(\frac{kg}{m^2 \ s}\) and so flow rate through "unit area" of surface with normal \(\hat n\) is \(\vec V \bullet \hat n\) which has units \(\frac{kg}{m^2 \ s}.\frac{m^2}{1}=\frac{kg}{s}\) http://www.amazon.co.uk/MathematicalMethodsPhysicalSciencesMary/dp/0471365807 it's only 34 pages so i'll copy them if you are using a different text. [and as it will come with a recommendation to buy, i reckon the copyright lawyers will forgive me.!]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0and how does \[V_{x}((x+dx),y,z)=V_{x}+\frac{\partial V_{x}}{\partial x}.dx\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0thanks, that was a lot helpful
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.