Water flows in a pipe of varying cross section kept horizontally. The mercury stands 12 cm at a point where the velocity of flow is 25 cm/s. Find the pressure at another point where the velocity is 100cm/s.

Solution

Bernoulli's theorem for the horizontal flow of liquid can be written as,

straight P subscript 1 over straight rho space plus space 1 half v subscript 1 squared space equals space P subscript 2 over rho space plus space 1 half v subscript 2 squared space

Here,
P₁= 12 cm of Hg
= 12 x 13.6 x 980 dyne/cm²P₂= ?
v₁= 25 cm/s,

v₂= 40cm/s
ρ = 1 gm/cc
Putting the values in equation (1), we have

fraction numerator 12 space cross times 13.6 cross times 980 over denominator 1 end fraction space plus space 1 half left parenthesis 24 right parenthesis squared space equals space P subscript 2 over 1 space plus space 1 half left parenthesis 100 right parenthesis squared space P subscript 2 space equals space 155224 space d y n e divided by c m squared space space space space space space equals 11.6464 space c m space o f space m e r c u r y space H g

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