Quoted: To find the answer to the first problem, look to the acceleration of the flow, which is just the first derivative of the velocity.
Can't help you with the second, need a reference. Besides, the fluid leaks out the edges of a channel. If it's a rectangular duct, that's another story.
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Because the velocity of the flow field is a function of position and time, you can't just take the first derivative of the velocity wrt time. You need to use partial differential equations. Using multivariable calculus, we can obtain the following:
acc=DV/Dt (capital Ds used for total derivatives, small ds used for partial)
if V=function(x,y,t), then DV/Dt=(dV/dx)(dx/dt)+(dV/dy)(dy/dt)+(dV/dt)
The last term (dV/dt) is known as local acceleration, which is acceleration due to changes in time. The first two terms (there would be a third if V was also a function of z) are convective acceleration, which is acceleration due to changes in position.
I believe the answer I gave above was correct.
By the way, it's almost certain that you WILL get a problem on your final exam where the flow is acclerating solely due to gravity and you'll be asked to determine local and convective acceleration. Here's a hint - one of them is zero. Can you guess which one?
P.S. If you'd give me a front pivot pin, detent and spring, I'd gladly pull out my books and solve the second problem for you.