Question 3 of 13: River Flow Accumulation and Level Rise

Question 3 — River Flow Accumulation and Level Rise (5 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given.

Find. The rate of storage accumulation, and the resulting rise in river level after 12 h.

Approach. Apply conservation of mass (control-volume continuity) to the reach between the bridges: accumulation rate = inflow − outflow; then convert accumulated volume to a level rise using the given surface area.

1. Accumulation rate. $$\frac{{dV}}{{dt}} = Q_{{in}}-Q_{{out}} = 55-45 = \boxed{{10\text{{ m}}^3/\text{{s}}}}$$
2. Volume accumulated in 12 h. $$V = 10\text{{ m}}^3/\text{{s}}\times(12\times3600\text{{ s}}) = 10\times43,200 = 432,000\text{{ m}}^3$$
3. Level rise. $$\Delta z = \frac{{V}}{{A}} = \frac{{432,000\text{{ m}}^3}}{{1.44\times10^6\text{{ m}}^2}} = \boxed{{0.300\text{{ m}} = 300\text{{ mm}}}}$$