Flow Development: Is psi = 4y - (y^3)/3 Fully Developed?

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The discussion focuses on determining whether the given stream function, psi = 4y - (y^3)/3, indicates a fully developed flow of water at 20°C. A flow is considered fully developed when there is no change in the velocity component in the flow direction, specifically when du/dx = 0. Participants seek guidance on how to analyze the stream function to assess flow development. The conclusion emphasizes that recognizing the condition of the velocity component is key to understanding flow development. Understanding these principles is essential for solving similar fluid dynamics problems.
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Homework Statement



The following stream function holds for a certain flow of water at 20 C.
psi = 4y - (y^3)/3.

Is this flow fully developed?

Homework Equations



psi = 4y - (y^3)/3.

The Attempt at a Solution



How am i suppose to tell if a flow is fully developed or not from the stream function? Direct me to what should i study to find the answer.
 
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I found the solution ..so here it is... for a flow to be fully developed, it should have no change in the u component. i.e. du/dx = 0
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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