Answer
$2.82\;m/s$
Work Step by Step
The flow around the barge is uniform. Therefore, we will use the equation of continuity to solve the problem.
Let, $ A_i$ is the cross-sectional area of the canal
$v_i$ is the initial water speed
$ A_b$ is the effective cross-sectional area of the canal at b
$v_b$ is the water speed at b
$A_iv_i=A_bv_b$
or, $HDv_i=[DH-db]v_b$
or, $v_b=\frac{HDv_i}{DH-db}$
Substituting the given values
$v_b=\frac{14\times55\times1.5}{55\times14-30\times12}\;m/s$
or, $v_b=2.82\;m/s$
Therefore, the water speed at b is $2.82\;m/s$
