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A problem on Bernoulli's theorem

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A liquid with a density of 1.37*10^3 kg/m^3 flows through two horizontal sections of tubing joined end to end. In the first section, the cross sectional area is 10.4cm^2, the flow speed is 276cm/sec, and the pressure is 1.42*10^5 Pa. In the second section, the cross sectional area is 2.71cm^2.

a) Calculate the flow speed in the smaller section in units of m/s.

b) Calculate the pressure in the smaller section in units of Pa.

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Solution Summary

The problem is solved using continuity equation and Bernoulli's theorem.

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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 ...

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