I would be very grateful if I could get some insight on how to resolve this. Con

Question

I would be very grateful if I could get some insight on how to resolve this.

Consider the following transition section: The flow from left to right is constant at Q = 12pi m3/s. What is the total acceleration of a water particle in the x-direction at x = 5m? Assume that the water is incompressible and that the x-component of velocity is uniform across each cross section. The flow of water from right to left is given by Q(t) = pit2 Calculate the total acceleration at x = 5m for t = 2 s. Make the same assumption as in part (a).

Explanation / Answer

Velocity of water = Q*area, area = pi*r^2, r = 6 - (x/10)*3,

Velocity of water = 12pi*pi*(6-0.3x)^2, accln = v*dv/dx ,

at x= 5m, v = 2398.3m/s, dv/dx = 24pi*pi*(6-0.3x)*(-0.3) = 319.775

so, accln = 766916.8m/s^2

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