Maximum obstruction height without upstream rise

An obstruction (hump) of height $\Delta z$ across the bed does not affect the upstream depth as long as the specific energy over it is at least the minimum, $E_{min}$. The limiting height is when the flow over the obstruction is just critical.

Given data

$b=2$ m, $Q=3$ m³/s, $y_1=1.5$ m.

$$q=\frac{3}{2}=1.5\ \text{m}^2/\text{s},\quad V_1=\frac{1.5}{1.5}=1.0\ \text{m/s}$$ $$E_1=y_1+\frac{V_1^2}{2g}=1.5+\frac{1.0^2}{19.62}=1.5510\ \text{m}$$

Critical condition at the obstruction

$$y_c=\sqrt[3]{\frac{q^2}{g}}=\sqrt[3]{\frac{1.5^2}{9.81}}=0.6121\ \text{m}$$ $$E_{min}=\frac32y_c=0.9182\ \text{m}$$

For no rise upstream, $E_1=E_{min}+\Delta z_{max}$:

$$\Delta z_{max}=E_1-E_{min}=1.5510-0.9182=0.633\ \text{m}$$

Answer: maximum height of the obstruction $=0.633$ m (about 63 cm). A higher obstruction will cause the upstream water level to rise.