A vessel 1.4 m wide and 2.0 m long is filled to a depth of 0.8 m with a liquid of mass density 8

step 1 Solving part A of this problem. So, here you can write the value of pressure is equal to rho g h

A vessel 1.4 m wide and 2.0 m long is filled to a depth of...

A vessel $1.4 \mathrm{m}$ wide and $2.0 \mathrm{m}$ long is filled to a depth of $0.8 \mathrm{m}$ with a liquid of mass density $840 \mathrm{kg} \mathrm{m}^{-3} .$ What will be the force in $\mathrm{N}$ on the bottom of the vessel $(a)$ when being accelerated vertically upwards at $4 \mathrm{m} \mathrm{s}^{-1},(b)$ when the acceleration ceases and the vessel continues to move at a constant velocity of $7 \mathrm{m} \mathrm{s}^{-1}$ vertically upwards? $$[(a) 25985 \mathrm{N},(b) 18458 \mathrm{N}]$$

Key Concepts

Pressure Force on Surfaces

The pressure force on any surface submerged in a fluid is determined by integrating the pressure distribution over that surface. For flat surfaces, this often simplifies to multiplying the pressure at a specific depth (usually at the bottom if the pressure is uniform over the area) by the area. This concept combines the effects of the pressure gradient and surface geometry to yield the total force exerted by the fluid.

Effective Gravitational Acceleration in Accelerating Frames

In a non-inertial reference frame, such as a vessel undergoing vertical acceleration, the effective gravitational acceleration is modified by the acceleration of the frame. For upward acceleration, the effective gravitational acceleration becomes the sum of the true gravitational acceleration and the acceleration of the vessel, thereby increasing the apparent weight of the fluid. This concept is vital for analyzing how pressure distribution changes in accelerating systems.

Hydrostatic Pressure

Hydrostatic pressure refers to the pressure exerted by a fluid at rest due to the force of gravity acting on it. This pressure increases linearly with depth because the weight of the fluid above exerts additional force on the lower layers. It plays a critical role in fluid statics and is usually expressed as the product of the fluid's density, gravitational acceleration, and depth.

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