L3 slide 7: Locating a point on an inclined plate (ENGR5002)

L3 slide 7: Locating a point on an inclined plateFrom lectureCurrent specThird4 marks5 min

L3 - Hydrostatic forces on submerged surfaces, slides 7-9 (a problem of coordinates)

A tank of water of depth $H$ and width $W$ is closed at one end by a flat plate of length $L$ , inclined at an angle $\theta$ to the free surface, running from the free surface down to the floor. A point $P$ lies on the wetted face of the plate.

The lecturer asks: how do we measure the position ("quota") of the point $P$ ?

Formulas you may need

Depth and distance along the plane: $z = l\sin\theta$ (learn this; slide 9)
Pressure at depth: $p(z) = p(z=0) + \rho g z$ (on the formula sheet)

(a)
Define the two coordinates that can be used for $P$ (absolute and relative), write the relation between them, and the relation between $H$ and $L$ . Which one sets the pressure at $P$ ?
[2]
(b)
[Added] $P$ is $l_P = 2.0$ m from the free surface measured along the plate, and $\theta = 30^\circ$ . Taking $\rho = 1000\ \mathrm{kg\,m^{-3}}$ and $g = 9.81\ \mathrm{m\,s^{-2}}$ , find the depth $z_P$ of $P$ and the gauge pressure there.
$z_{P}$ =
m
$p_{\mathrm{gauge}}$ at $P$ =
kPa
[2]