Consider the following transition section:

$(1)$ If the flow of water from left to right is constant at $Q=0\mathrm{.}1\frac{m^3}{s},$ what is the total

acceleration of a water particle at $x=0\mathrm{.}5m?$ Assume that the water is incompressible, and

that the $x$ component of velocity is uniform across each cross section.

$(2)$ The flow of water from right to left is expressed by

$Q(t)=\frac{t^2}{100}$

Calculate the total acceleration at $x=0\mathrm{.}5m$ for $t=4\mathrm{.}48s.$ Make the same assumptions as

in part $($a$).$