Therefore, the speed of the liquid increases as it passes through the constriction. Since the meter is assumed to be horizontal.
Thus, as the fluid passes through the constriction or throat, the higher speed results in lower pressure at the throat. The expression for the continuity equation is,
A1v1=A2v2
Here, A1andA2 are the cross-sectional areas at the inlet and outlet, respectively, and
V1, V2 are the velocity of the fluid at the inlet and outlet, respectively
Let,
A1
and A2be the cross-sectional areas at point 1 and 2, respectively, andv1, v2be the corresponding flow speed.
Express the relation for the continuity equation.
A1v1=A2v2..........................(1)
Now apply proportionate rule,
v2v1=A1A2>1(∵A1>A2)
Therefore, the speed of the liquid increases as it passes through the constriction. Since the meter is assumed to be horizontal.
Now, according to Bernoulli’s equation, we get,
p1+12ρv12=p2+12ρv22p1−p2=12ρ[v22−v12]p1−p2=12ρv12[(v2v1)2−1]p1−p2=12ρv12[(A1A2)2−1]
Again, Since
A1>A2
the bracketed term is positive, so thatp1>p2. Thus, as the fluid passes through the constriction or throat, the higher speed results in lower pressure at the throat.
