Question

two dimensional flow and explanation with diagram
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Answer 1

Step-by-step explanation:

when the flow velocity at every point is parallel to a fixed plane. The velocity at any point on a given normal to that fixed plane should be constant.

Answer 2

Step-by-step explanation:

Fluid motion can be said to be a two-dimensional flow when the flow velocity at every point is parallel to a fixed plane. The velocity at any point on a given normal to that fixed plane should be constant.

Flow velocity in Cartesian co-ordinates Edit

Considering a two dimensional flow in the {\displaystyle X-Y} {\displaystyle X-Y} plane, the flow velocity at any point {\displaystyle (x,y,z)} (x,y,z) at time {\displaystyle t} t can be expressed as –

{\displaystyle {\bar {\boldsymbol {v}}}(x,y,z,t)=v_{x}(x,y,z,t){\hat {\boldsymbol {i}}}+v_{y}(x,y,z,t){\hat {\boldsymbol {j}}}.} {\displaystyle {\bar {\boldsymbol {v}}}(x,y,z,t)=v_{x}(x,y,z,t){\hat {\boldsymbol {i}}}+v_{y}(x,y,z,t){\hat {\boldsymbol {j}}}.}

Velocity in cylindrical co-ordinates Edit

Considering a two dimensional flow in the {\displaystyle r-\theta } {\displaystyle r-\theta } plane, the flow velocity at a point {\displaystyle (r,\theta ,z)} (r,\theta,z) at a time {\displaystyle t} t can be expressed as –

{\displaystyle {\bar {\boldsymbol {v}}}(r,\theta ,z,t)=v_{r}(r,\theta ,z,t){\hat {\boldsymbol {r}}}+v_{\theta }(r,\theta ,z,t){\hat {\boldsymbol {\theta }}}.} {\displaystyle {\bar {\boldsymbol {v}}}(r,\theta ,z,t)=v_{r}(r,\theta ,z,t){\hat {\boldsymbol {r}}}+v_{\theta }(r,\theta ,z,t){\hat {\boldsymbol {\theta }}}.}