A two dimensional fluid element rotates like a rigid body. At a point with in the element, the pressure is $$1$$ unit. Radius of the Mohr's circle, charactering the state of stress at the point, is

The pressure gauges $${G_1}$$ and $${G_2}$$ installed on the system shown pressures of $${P_{G1}} = 5.00$$ bar and $${P_{G2}} = 1.00$$ bar. The value of unknown pressure $$P$$ is

The pressure gauges $${G_1}$$ and $${G_2}$$ installed on the system show pressures of $${P_{G1}} = 5.00$$ bar and $${P_{G2}} = 1.00$$ bar. The value of unknown pressure $$P$$ is

The horizontal and vertical hydrostatic forces $${F_x}$$ and $${F_y}$$ on the semi-circular gate, having a width $$'w'$$ into the plane of figure, are