Question

A closed tank is filled with water and has a 4-ft-diameter hemispherical dome as shown in Fig. P2.129. A U-tube manometer is connected to the tank. Determine the vertical force of the water on the dome if the differential manometer reading is 7 ft and the air pressure at the upper end of the manometer is 13.4 psi.

Answer 1

Concepts and reason

Pressure:

The pressure is defined as the force acting per unit area.SI unit of pressure is .

Manometer:

The pressure of a fluid is measured using manometer device. It measures gauge pressure, differential pressure, and absolute pressure. It displays pressure in an integral unit.

Fundamentals

The general formula to calculate the pressure is given as,

$P=pgh $

Here pressure is , density is , acceleration due to gravity is , and height is .

In resolving the forces as horizontal forces and vertical forces, the trigonometric angle of sine is considered only in vertical direction and the trigonometric angle of cosine is considered only in horizontal direction.

The equilibrium of force along the vertical direction is given as follows.

Draw the schematic diagram as in figure .

Write the relation of pressure from the left side of the manometer ()

Here, pressure of air is , specific gravity of gauge fluid is, specific gravity of water fluid is , height of gauge fluid is , height of water fluid is , density of gauge fluid is, and acceleration due to gravity is.

Substitute for, for , for , for , for , for , and for .

Draw the free body diagram of the dome as in figure .

Write the equilibrium of force along the vertical direction.

Substitute for , for and for .

Ans:

The vertical force exerted by water on the dome is.