Question

The velocity field of a given flow in Cartesian coordinates can be expressed as V = (5z − 3)ˆi + (x + 3)ˆj + 4ykˆ ft/s, where x, y, and z are in feet. Determine the fluid speed at the origin (0, 0, 0) and along the x-axis (y = z = 0).

Answer 1

The fluid speed along the origin is
`|v| =  5\  ft /s`

The fluid speed of along x-axis(y = z = 0) is
`|v| =  √( 9 + (x +4)^2) \ ft/s`

Step-by-step explanation:

From the question we are told that

The velocity is
`v  =  (5z -3)i + (x + 4 )j + 4yk`

Generally at origin
`x = 0 \  m ,  \   y = 0\  m  \ ,  z = 0 \  m`

So at the origin the equation becomes

`v = -3i + 4j  +0k`

Generally the magnitude of the speed at origin is mathematically represented as

`|v| =  √( (-3)^2 +  (4)^2 + (0)^2)`

=>
`|v| =  5\  ft /s`

Generally the velocity on the x- axis ( y= z = 0 ) is mathematically represented as

`v = -3i + (x + 4)j`

Generally the magnitude of the speed is

`|v| =  √( (-3)^2 + (x +4)^2)`

`|v| =  √( 9 + (x +4)^2) \ ft/s`