For the velocity field given by u - V cos- and v - V sin- and w - 0 - where V and - are constant- the stream lines are-

Dxu= dyv = dzw dxV cosθ = dyV sinθ = dz0 dydx = V sinθV cosθ = tanθ y = x tanθ nbsp; + C Hence the streamlines are straight and inclined at angle θ ...

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Fluid Mechanics

Streamline , Streakline and Pathline

For the veloc...

Question

For the velocity field given by $u = V cos θ$ and $v = V sin θ$ and $w = 0$ , where $V$ and $θ$ are constant, the stream lines are:

Straight

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Parabolic

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Elliptical

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None of above

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Solution

The correct option is A Straight
$\frac{d x}{u} = \frac{d y}{v} = \frac{d z}{w}$

$\frac{d x}{V cos θ} = \frac{d y}{V sin θ} = \frac{d z}{0}$

$\frac{d y}{d x} = \frac{V sin θ}{V cos θ} = tan θ$

$y = x tan θ + C$

Hence the streamlines are straight and inclined at angle $θ$

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For the velocity field given by u=Vcosθ and v=Vsinθ and w=0 , where V and θ are constant, the stream lines are:

The correct option is A Straightdxu=dyv=dzw dxVcosθ=dyVsinθ=dz0 dydx=VsinθVcosθ=tanθ y=xtanθ+C Hence the streamlines are straight and inclined at angle θ

For the velocity field given by $u = V cos θ$ and $v = V sin θ$ and $w = 0$ , where $V$ and $θ$ are constant, the stream lines are:

The correct option is A Straight
$\frac{d x}{u} = \frac{d y}{v} = \frac{d z}{w}$

$\frac{d x}{V cos θ} = \frac{d y}{V sin θ} = \frac{d z}{0}$

$\frac{d y}{d x} = \frac{V sin θ}{V cos θ} = tan θ$

$y = x tan θ + C$

Hence the streamlines are straight and inclined at angle $θ$