Question

Why does the speed of a liquid increase and its pressure decrease when a liquid passes through constriction in a horizontal pipe?

Answer 1

Consider a horizontal constricted tube. Let A₁ and A₂ be the cross-sectional areas at points 1 and 2, respectively. Let v₁ and v₂ be the corresponding flow speeds, ρ is the density of the fluid in the pipeline. By the equation of continuity,

v₁A₁ = v₂ A₂ …… (1)

\(\therefore\) \(\cfrac{v_2}{v_1} = \cfrac{A_1}{A_2}\)> 1(\(\because\) A₁ > A₂)

Therefore, the speed of the liquid increases as it passes through the constriction. Since the meter is assumed to be horizontal, from Bernoulli’s equation we get,

Again, since A₁ > A₂ , the bracketed term is positive so that p₁ > p₂ . Thus, as the fluid passes through the constriction or throat, the higher speed results in lower pressure at the throat.