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 P₁ and P₂, respectively.

Let v₁ and v₂ be the corresponding flow speeds.

ρis the density of the fluid in the pipeline.

By the equation of continuity,

A₁v₁ = A₂v₂     ... (1)

v₂/ v₁ =A₁/A₂ > 1    (…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,

\(p_1+\frac{1}{2}ρv_1^2\) =\(p_2+\frac{1}{2}ρv_2^2\) 

\(p_1+\frac{1}{2}ρv_1^2\) =\(p_2+\frac{1}{2}ρv_1^2(\frac{A_1}{A_2})^2\) 

 \(p_1-p_2=\frac{1}{2}ρv_1^2\left[(\frac{A_1}{A_2})^2-1\right]\) 

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.