[Help] Fluid flow through a cone
November 17, 2010 at 4:47 pm
(This post was last modified: November 17, 2010 at 4:48 pm by Autumnlicious.)
The principle of equivalency is:
![[Image: latex2png.2.php?z=100&eq=%5Cfrac%7B%5Cpa...ial%20x%7D]](https://images.weserv.nl/?url=www.sitmo.com%2Fgg%2Flatex%2Flatex2png.2.php%3Fz%3D100%26amp%3Beq%3D%255Cfrac%257B%255Cpartial%2520%255Crho%257D%257B%255Cpartial%2520t%257D%2520%253D%2520-%255Cfrac%257B%255Cpartial%2520%255Crho%2520v%257D%257B%255Cpartial%2520x%257D)
The structure is a Pipe, with:
v(x) as a function of x.
![[Image: latex2png.2.php?z=100&eq=A(x)%20%3D%20A_...%7Bx_0%7D)]](https://images.weserv.nl/?url=www.sitmo.com%2Fgg%2Flatex%2Flatex2png.2.php%3Fz%3D100%26amp%3Beq%3DA%28x%29%2520%253D%2520A_0%2520%281%2520%252B%2520%255Cfrac%2520%257Bx%257D%257Bx_0%257D%29)
Density (rho) is constant.
Find Mass flow (kg/s) into the pipe with cross section A at x=0. Assume Mass flow does not variate, by neither v or A, aka Mass flow is constant.
Find x such that:
![[Image: latex2png.2.php?z=100&eq=v(x)%20%3D%20%5...2%7D%20v_0]](https://images.weserv.nl/?url=www.sitmo.com%2Fgg%2Flatex%2Flatex2png.2.php%3Fz%3D100%26amp%3Beq%3Dv%28x%29%2520%253D%2520%255Cfrac%2520%257B1%257D%257B2%257D%2520v_0)
What I did was define for Mass flow into the element of pipe:
![[Image: latex2png.2.php?z=100&eq=M(x%3D0)%20%3D%...0v_0%20A_0]](https://images.weserv.nl/?url=www.sitmo.com%2Fgg%2Flatex%2Flatex2png.2.php%3Fz%3D100%26amp%3Beq%3DM%28x%253D0%29%2520%253D%2520%255Crho%2520v_0%2520A%28_%257Bx%253D0%257D%29%2520%253D%2520%255Crho%2520v_0%2520A_0)
Keeping Mass flow constant but changing x, I found that M(0) = M(x) s.t.
![[Image: latex2png.2.php?z=100&eq=%20%5Crho_0%20v...%7Bx_0%7D)]](https://images.weserv.nl/?url=www.sitmo.com%2Fgg%2Flatex%2Flatex2png.2.php%3Fz%3D100%26amp%3Beq%3D%2520%255Crho_0%2520v_0%2520A_0%2520%253D%2520%255Crho%2520_0%2520%255Cfrac%2520%257B1%257D%257B2%257Dv_0%2520A_0%281%252B%2520%255Cfrac%2520%257Bx%257D%257Bx_0%257D%29)
Making x=x_0 for v(x) = .5 v_0
This seemed too easy. One thought is that I defined M(0) wrong.
The structure is a Pipe, with:
v(x) as a function of x.
Density (rho) is constant.
Find Mass flow (kg/s) into the pipe with cross section A at x=0. Assume Mass flow does not variate, by neither v or A, aka Mass flow is constant.
Find x such that:
What I did was define for Mass flow into the element of pipe:
Keeping Mass flow constant but changing x, I found that M(0) = M(x) s.t.
Making x=x_0 for v(x) = .5 v_0
This seemed too easy. One thought is that I defined M(0) wrong.
