# Bernoulli's Theorem

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Water at a pressure of 3.8 atm at street level flows into an office building at a speed of 0.50 m/s through a pipe 4.2 cm in diameter. The pipes taper down to 2.6 cm in diameter by the top floor, 20 m above (in figure). Calculate the flow velocity and the pressure in such a pipe on the top floor. Ignore viscosity. Pressures are gauge pressures.

flow velocity

______m/s

pressure

______atm

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##### Solution Summary

The pressures in the pressure gauge are calculated using Bernoulli's theorem. A step by step solution provided.

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SOLUTION

Basic theory

Continuity equation : Assuming the liquid to be incompressible, rate of flow of liquid (that is volume of liquid flowing per sec) at any cross section is same. If the velocity of the liquid at any cross section is v, the liquid will move forward by a distance equal to v in 1 second at that cross section and area of cross section x velocity gives the volume of liquid flowing per sec. at that cross section.

Thus, as per the continuity principle, av = constant (a1v1 = a2v2 = a3v3 etc.) where a = area of cross section, v = velocity of liquid at that cross section. ........(1)

Bernoulli's theorem : For streamline flow of a perfect liquid in a pipe*, the sum of pressure energy, ...

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