Hydrostatic Pressure and Buoyancy Equations: Applications and Calculations, Exercises of Engineering

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Hydrostatic pressure equation

Pressure anywhere at the same depth in a liquid must be the same.

T-shaped cylinder

An open-bottomed cylinder (shown below) sits on a table. What is the minimum weight of

the cylinder which will allow it to stay on the table when it is filled with water?

Pythagoras cup

Barometers

The height difference between the vacuum and the end that is open to the atmosphere tells

us the atmospheric pressure.

Archimedes’ principle

Work out the proportion of the object that will be submerged

Variation in pressure given a variation in temperature

As seen in the figure on the previous page, the temperature varies linearly for the first 11,

m above sea level (the Troposphere), so

Where 𝐶 is a constant. Calculate the resulting change in pressure with altitude.

Weather balloon

A spherical balloon of 8 m diameter and mass 60 kg is filled with Helium and released from its

mooring at sea level. Find the height to which the balloon will rise, assuming that the balloon

does not stretch, and that the air obeys the international standard atmosphere:

𝑇A =𝑇SL −𝐶𝑧 where 𝐶=0.0065Kelvin/metre, and𝑇 =288K 𝐴 𝑆𝐿 𝑆𝐿

And,

, where 𝜌 𝑆𝐿

=1.225 kg/m

Take the density of helium, 𝜌𝐻𝑒, to be 0.17 kg/m

Force on a submerged wall (e.g., a dam)

A swimming pool is built with a sloping floor section near one wall. The depth of the water at

the wall, H, is 3 m, while the sloping section AB has length,

L = 5 m and angle 𝜃 = 30°. Find the resultant force on the wall AB due to hydrostatic pressure

and its line of action.

Take the density of water, 𝜌, to be 1000 kg/m

Work out mass flow

Consider, first of all, a liquid of density r coming out of a square pipe at uniform speed V:

Flow is at an angle to the pipe

Consider a jet coming out of a hole in a wall with a flow angle 30

o to the vertical, as shown

below.

Non uniform flow: between 2 plates

Non uniform flow: Cylindrical pipe

Control volume example 3: Wind turbine

The wind speed far upstream of a 55 m diameter wind turbine is 12 m/s. Far downstream,

the wake is uniform and 8 m/s. Take the density of air to be 1.22 kg/m

Control volume example 4: The wake of a submarine

A submarine is travelling at U m/s. It leaves a wake of radius R and profile,