A tank with a flat bottom of area A and vertical sides is...

A tank with a flat bottom of area $A$ and vertical sides is filled to a depth $h$ with wath water. The pressure is 1 atm at the top surface. (a) What is the absolute pressure at the bot- tom of the tank? (b) Suppose an object of mass $M$ and density less than the density of water is placed in the tank and floats. No water overflows. What is the resulting increase in pressure at the bottom of the tank? (c) Evalu- ate your results for a backyard swimming pool with depth 1.50 $\mathrm{m}$ and a circular base with diameter 6.00 $\mathrm{m}$ . Two persons with combined mass 150 $\mathrm{kg}$ enter the pool and float quietly there. Find the original absolute pressure and the pressure increase at the bottom of the pool.

A tank with a flat bottom of area $A$ and vertical sides is filled to a depth $h$ with wath water. The pressure is 1 atm at the top surface. (a) What is the absolute pressure at the bot- tom of the tank? (b) Suppose an object of mass $M$ and density less than the density of water is placed in the tank and floats. No water overflows. What is the resulting increase in pressure at the bottom of the tank? (c) Evalu-
ate your results for a backyard swimming pool with depth 1.50 $\mathrm{m}$ and a circular base with diameter 6.00 $\mathrm{m}$ . Two persons with combined mass 150 $\mathrm{kg}$ enter the pool and float quietly there. Find the original absolute pressure and the pressure increase at the bottom of the pool.

Key Concepts

Hydrostatic Pressure

Hydrostatic pressure refers to the pressure exerted by a fluid at equilibrium due to the force of gravity. It increases linearly with depth according to the equation P = ?gh, where ? is the fluid density, g is gravitational acceleration, and h is the depth. This concept is fundamental in understanding how pressure varies in a fluid column.

Absolute vs. Gauge Pressure

Absolute pressure is the total pressure measured from a perfect vacuum, while gauge pressure is relative to atmospheric pressure. In fluid statics, it is important to distinguish between the two because many problems involve calculating pressures that incorporate atmospheric pressure (absolute pressure) or just the additional pressure due to the fluid column (gauge pressure).

Buoyancy and Floating Objects

Buoyancy arises from the pressure difference across a submerged or floating object, leading to an upward force equal to the weight of the displaced fluid, as stated by Archimedes’ principle. When an object floats, it displaces a volume of fluid whose weight equals the weight of the object. This principle helps determine how an added mass changes the force distribution in the fluid.

Pressure Increase due to Added Load

When an additional load is introduced into a fluid system (for example, by placing a floating object), its weight is supported by the fluid through an increase in the fluid level or pressure. The extra pressure at the bottom of the container is directly related to the added force distributed over the cross-sectional area, typically calculated by dividing the extra weight by the area of the base.

Transcript

00:01 Everyone this is the problem based on static pressure.

00:04 Here it is given.

00:06 Water is filled in a container having flats bottom surface of area a to the height edge.

00:39 In the first part we have to calculate absolute pressure at the bottom of the container.

00:47 B part we have to calculate increase in pressure at the bottom if a body of mass mkg having density less than water and there is no overflow of water in sea part we have to evaluate pressure at bottom and change in pressure for in a swimming pool water is to be filled up to the height of 150 meter bottom having the circular surface of diameter 6 2 swimmers each combined mass 150 kg is swimming let us say a first part at bottom pressure will be atmospheric pressure plus pressure due to weight of water filled in it be atmospheric weight of water will be mass of water filled into g upon a now mass of water fill volume into density volume will be area into height into g volume into density let me correct mass will be volume into density volume will be area into height up to which liquid is filled into density into g upon a so on solving it absolute pressure at the bottom of container you will get p atmospheric plus h -r -g so this is the answer of part a in part b if a body is submerged in the water having density less than that of water then water then water will rise in the tank so that weight of volume displaced weight of volume volume of water displaced is equal to weight of the body hence at the bottom force will increase by gets increased by weight of the body that is empty hence increased pressure at the bottom will be m g by a.

05:14 Now see part.

05:17 We have to calculate the pressure at the bottom for water to be filled up to the height of 150 meter in the swimming pool...

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