How Is Angular Momentum Calculated Without Considering Gravity and Viscosity?

[Est120]

Homework Statement

write the macroscopic angular momentum balance for the following problem

Relevant Equations

see image

we neglect gravity and viscosity efects
i really can't understand how does the author managed to get the equation in the image

 

[haruspex]

Not making any sense to me either.
Altitude at $\frac 12b_1$ from where?
$b_1$ is at an angle, so $b_1-b_{2a}$ doesn’t seem right.
And what about the force from the plate? We don't know where that is centred, so we can't set the axis so as to eliminate its torque.

 

[Est120]

it's an idealized problem, all i need to know is how they compute the cross product , there is no viscosity so there is no friction with the plate

 

[haruspex]

how they compute the cross product

For that, I need you to define the r and u vectors in the boxed equation.

there is no friction with the plate

It's not to do with friction. The incoming flow exerts a vertically downward force $w_1v_1$ on the plate. The reaction from the plate likely has a torque about the chosen axis.