Fluid Statics · Fluid Mechanics · GATE ME

For a floating body, buoyant force acts at the

For a completely submerged body with centre of gravity $$‘G’$$ and centre of buoyancy $$‘B’,$$ the condition of stability will be

For a completely submerged body with center of gravity $$'G'$$ and center of buoyancy $$'B',$$ the condition of stability will be

For the stability of a floating body, under the influence of gravity alone, which of the following is TRUE?

A cylindrical body of cross - sectional area A, height $$H$$ and density $${\rho _s},$$ is immersed to a depth $$h$$ in a liquid of density $$\rho ,$$ and tied to the bottom with a string. The tension in the string is

A static fluid can have

A mercury manometer is used to measure the static pressure at a point in a water pipe as shown in Fig. The level difference of mercury in the two limbs is $$10$$ $$mm.$$ The gauge pressure at that point is

Bodies in floatation to be in stable equilibrium the necessary and sufficient condition is that the center of gravity is located below the _____________

Shown below are three cylindrical gates which restrain water in $$2$$-$$D$$ channel. Which gate experiences the maximum vertical component, the minimum vertical component and the maximum horizontal component of the hydrostatic force?

The figure shows two fluids held by a hinged gate. The atmospheric pressure is P_a = 100 kPa. The moment per unit width about the base of the hinge is ____________ kNm/m. (Rounded off to one decimal place)

Take the acceleration due to gravity to be g = 9.8 m/s².

A uniform wooden rod (specific gravity = 0.6, diameter = 4 cm and length = 8 m) is immersed in the water and is hinged without friction at point A on the waterline as shown in the figure. A solid spherical ball made of lead (specific gravity = 11.4) is attached to the free end of the rod to keep the assembly in static equilibrium inside the water. For simplicity, assume that the radius of the ball is much smaller than the length of the rod.

Assume density of water = 10³ kg/m³ and π = 3.14.

Radius of the ball is _______ cm (round off to 2 decimal places).

For the stability of a floating body the

The large vessel shown in the figure contains oil and water. A body is submerged at the interface of oil and water such that $$45$$ percent of its volume is in oil while the rest is in water. The density of the body is _______________ $$kg/{m^3}.$$

The specific gravity of oil is $$0.7$$ and density of water is $$1000$$ $$kg/{m^3}.$$

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

Consider a frictionless, massless and leak-proof plug blocking a rectangular hole of dimensions $$2R \times L$$ at the bottom of an open tank as shown in the figure. The head of the plug has the shape of a semi-cylinder of radius $$R.$$ The tank is filled with a liquid of density $$\rho $$ up to the tip of the plug. The gravitational acceleration is $$g.$$ Neglect the effect of the atmospheric pressure.

The force $$F$$ required to hold the plug in its position is

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

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 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 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

In given figure, if the pressure of gas in bulb $$A$$ is $$50$$ $$cm$$ $$Hg$$ vacuum and $${P_{atm}} = 76\,cm\,Hg,$$ then height of column $$H$$ is equal to

Refer to figure, the absolute pressure of gas $$A$$ in the bulb is

The force $$F$$ needed to support the liquid of density $$d$$ and the vessel on top (fig) is

The cross-sectional area of one limb of a U-tube manometer [ Figure shown below ] is made $$500$$ time larger than the other, so that the pressure difference between the two limbs can be determined by measuring $$'h'$$ on one limb of the manometer. The percentage error involved is :

A circular plate $$1$$ $$m$$ in diameter is submerged vertically in water such that its upper edge is $$8m$$ below the free surface of water. The total hydrostatic pressure force on one side of plate is :

A cylinder of mass $$10$$ kg and area of cross-section $$0.1$$ $${m^2}$$ is tied down with string in a vessel containing two liquids as shown in Figure. Calculate gauge pressure on the cylinder bottom and the tension in the string. Density of water $$ = 1000\,\,kg/{m^3}.$$ Specific gravity of $$A=0.8$$. Specific gravity of $$B$$ (water) $$=1.0$$