Answer to Question #278939 in Classical Mechanics for joseph

Question

1. Determine the discharge over an uncontracted horizontal weir that is 1.5 m high and 4.5 m long. The upstream depth is 2.2 m. Determine the Ink height if the same discharge was desired without exceeding an upstream depth of 1.8 m?

2. Determine the discharge over a standard contracted weir when the upstream water depth is 2.1 m. The weir (one end contraction) is 1.8 m high and has a 1.8 m overflow length. Also determine the approach velocity head in the 4-m-wide channel. Is it significant?

Answer 1

1.

$Q=\frac{Q_0}4=0.0015~\frac{m^3}s,$

$v=\frac QA=\frac Q{\pi r^2}=29.8~\frac ms,$

$\omega=\frac v l=99.5~\frac {rad}s.$

2.

$F=pA,$

$A=\pi r^2,$

$p=\frac{\rho v^2}2,$

$F=\frac{\pi r^2\rho v^2}2=855~N.$