An inverted U-tube manometer is used to measure the pressure difference between two pipes $$A$$ and $$B,$$ as shown in the figure. Pipe $$A$$ is carrying oil (specific gravity $$= 0.8$$) and pipe $$B$$ is carrying water. The densities of air and water are $$1.16\,\,kg/{m^3}$$ and $$1000\,\,kg/{m^3},$$, respectively. The pressure difference between pipes $$A$$ and $$B$$ is _______________$$kPa.$$

$$Acceleration$$ $$due$$ $$to$$ $$gravity$$ $$g = 10\,m/{s^2}$$

A spherical balloon with a diameter of $$10m,$$ shown in the figure below is used for advertisements. The balloon is filled with helium $$\left( {{R_{He}} = 2.08\,\,\,\,kJ/kg.K} \right)$$ at ambient conditions of $${15^ \circ }C$$ and $$100\,\,kPa.$$ Assuming no disturbances due to wind , the maximum allowable weight (in Newton) of ballon material and rope required to avoid the fall of the balloon $$({R_{air}} = 0.289kJ/kg.K)$$ is _____________.

A hinged gate of length $$5$$ $$m,$$ inclined at $${30^ \circ }$$ with the horizontal and with water mass on its left, is shown in the figure below. Density of water is $$1000$$ $$kg/{m^3}$$. The minimum mass of the gate in kg per unit width (perpendicular to the plane of paper), required to keep it closed is

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