Question
Water at a pressure of flows at 2.0 m/s through a pipe of 0.02 m^{2} crosssectional area which reduces to 0.01 m^{2}. What is the pressure in the smaller in the crosssection of the pipe?

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diffcult
Solution
Let us consider a horizontal pipe of nonuniform crosssection through which water is flowing. By the principle of continuity, if at one place the area of cross section is A_{1} and the velocity of water v_{1}; and at another place the area of crosssection is A_{2} and the velocity of water is v_{2}, then
Substituting the given values :
= 4.0 m/s.
If the pressure of water in the crosssectional area A_{1} is P_{1} and in A_{2} is P_{2}, then by Bernoulli’s theorem :
where is density of water (= 10^{3} kg/m^{3}).
Here,
.
Substituting this in eq. (i), we have
.
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