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Draw pressure charts and calculate the value of pressure. Tank width b=2m.

The valve with a radius of R=1 m and a length of L=10 m closes the corner of a rectangular tank as shown in the figure. Determine the moment that should be applied to keep the valve in the closed position if the tank is filled with water with a density of ρw=1 g/cm^3, while the density of the material from which the valve is made is ρz=5 g/cm^3.

How many times must the density of liquid no. 2 be greater than the density of liquid no. 1 for equilibrium to occur? The width of the container is \( b=1m \).

In the side wall of the tank, which is under pressure \( p_n = 4905 Pa \), there is a hole. The hole is closed by a flat flap with a width of L using a float in the shape of a cone with a height of d connected to a half of a sphere with a radius of r. The flap can rotate relative to point O. The float has a mass m. The elevation of the vertex of the float above the axis of rotation of the flap is b. The vertex of the float is submerged at a depth of a. What volume V must the float have to ensure the closure of the hole as shown in the picture?
Data: \( a=0.25m, b=0.75m, d=0.5m, m=10kg, \rho_{H_2O} = 1000 kg/m^3, L=0.5m, p_n=4905Pa \)

A square flap with a weight G covers the outlet of a water tank. The flap has a pivot axis O. Determine the vertical force F needed to lift the flap.
Data:
\begin{aligned} &h_1 = 3.5 m\\ &h_2 = 2.5 m\\ &G = 200 N\\ &\alpha = 30^{\circ}\\ \end{aligned}

The tank is closed with a quarter-cylinder-shaped rotating flap with a radius R=1m and length L=1m. Determine the magnitude of the hydrostatic pressure exerted on the flap for two variants shown in the figure. The density of water \(\rho = 1000 kg/m^3\), the height of water in the tank H=2m.

Calculate the pressure of water on the surface AB of the closure with the shape shown in the figure. Data: \begin{aligned} &D = 2m\\ &B = 5m\\ \end{aligned}

In the side wall of the tank, where there is an overpressure (\( p_n = 200 hPa \)), there is a rectangular opening with dimensions \( a \times a/2 \). The opening is closed with a flat flap using a float in the shape of a prism with a regular hexagonal base of side length c and height f. The float has a mass of \( m_p = 10 kg \). The water elevation above the axis of rotation of the flap is \( H \). What volume \( V \) must the float have in order to ensure the closure of the opening when the float is completely submerged?
Data:
\begin{aligned} &a=0.8 m\\ &b=1 m \\ &c=0.7 m\\ &H =2 m\\ \end{aligned}

For the layout shown in the figure, calculate the value of pressure, position of the point of action, and angle at which the pressure force acts.
\begin{aligned} & \rho=1000 \frac{\mathrm{kg}}{\mathrm{m}^3} \\ & g=9.81 \frac{m}{s^2} \\ & \gamma=\rho \cdot g=9810 \frac{N}{m^3} \\ & h=1 m \\ & b=1 m \end{aligned}

A valve in the shape of a \(1 / 4\) of a cylinder, made of a material with a density of \(\rho_{\mathrm{z}}=7 \mathrm{~g} / \mathrm{cm}^3\), can rotate around the "O" axis to close a rectangular pipe with a width of \(\mathbf{B}=\mathbf{2} \mathbf{R}\) and a height of \(\mathbf{R}=\mathbf{1 m}\), through which water can flow out of the pool. Determine the value of the force \(\boldsymbol{P}\) necessary to keep the valve in the closed position, if the pool is filled with water to a height of \(3 R\). Assume the density of water to be \(\rho=1 \mathrm{~g} / \mathrm{cm}^3\).