Glycerine flows through a conical section of a pipe, with the cross sectional area at its two ends as 1 m2 and 4 m2. The pressure drop across the ends of a pipe is 10 N/m2. Calculate the velocity of at narrow end.
According to Bernoulli's theorem the pressure drop is given as [straight pipe]
ΔP = (1/2).ρ.[v12 - v22] ...............................(1)
and also
a1v1 = a2v2
or
velocity at thicker end
v2 = a1v1 / a2
here,
a1 = 1m2
a2 = 4m2
so,
v2 = (1/4).v1
thus, (1) become
ΔP = (1/2).ρ.[v12 - ((1/4)v1)2]
or
ΔP = (1/2).ρ.(15/16)v12
or
v12 = (16/15).[2ΔP/ρ]
here,
ΔP = 10N/m2
ρ (for glycerine) = 1.25x10 3 kg/m3
so,
v1 can be calculated...