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Fluid Mechanics

Continuity Equation-II

Water flows t...

Question

Water flows through pipe with a velocity given by
$\to V = (\frac{4}{t} + x + y)^j m / s$ ,
where $^j$ is the unit vector in the y direction, t(>0) is in second, and x and y are in meters. The magnitude of total acceleration at the point (x,y)= (1,1) at t=2s is_____ $m / s^{2}$

3

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Solution

The correct option is A 3
$\to V = (\frac{4}{t} + x + y)^j$

$a = \sqrt{/ a_{x}^{2} + a_{y}^{2} + / a_{z}^{2}}$

$a = a_{y}$

$a_{y} = v \frac{\partial v}{\partial y} + \frac{\partial v}{\partial t} = a$

at x = 1; y = 1; t = 2

$a = 3 m / s^{2}$

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Water flows through pipe with a velocity given by →V=(4t+x+y)^j m/s, where ^j is the unit vector in the y direction, t(>0) is in second, and x and y are in meters. The magnitude of total acceleration at the point (x,y)= (1,1) at t=2s is_____ m/s2 3

The correct option is A 3→V=(4t+x+y)^j a = √/a2x+a2y+/a2z a = ay ay=v∂v∂y+∂v∂t=a at x = 1; y = 1; t = 2 a=3m/s2

Water flows through pipe with a velocity given by
$\to V = (\frac{4}{t} + x + y)^j m / s$ ,
where $^j$ is the unit vector in the y direction, t(>0) is in second, and x and y are in meters. The magnitude of total acceleration at the point (x,y)= (1,1) at t=2s is_____ $m / s^{2}$

3

The correct option is A 3
$\to V = (\frac{4}{t} + x + y)^j$

$a = \sqrt{/ a_{x}^{2} + a_{y}^{2} + / a_{z}^{2}}$

$a = a_{y}$

$a_{y} = v \frac{\partial v}{\partial y} + \frac{\partial v}{\partial t} = a$

at x = 1; y = 1; t = 2

$a = 3 m / s^{2}$