[Fluid Mechanics] Venturimeter
By: Tao Steven Zheng（鄭濤）
【Problem】
Consider an ideal fluid of density flowing through a horizontal pipe of variable cross-sectional area. The fluid at the portion of the pipe with cross-sectional area
is moving at
and has a measured pressure of
. The fluid at the portion of the pipe with cross-sectional area
is moving at
and has a measured pressure of
.
Part 1: Determine in terms of
.
Part 2: Two different fluids of density (fluid in the horizontal pipe) and
(fluid in the u-shaped manometer), where
. The height difference of the fluid in the manometer is
. It helps to let
. Determine
in terms of
.
【Solution】
Part 1
There are two important equations for this problem:
1) The continuity equation
2) Bernoulli’s equation
From the first equation we find
Since there is no change in the altitude of the pipe; hence,
Isolate for :
Part 2
Treat the manometer as two static column problems.
Substitute the difference of pressure into the result from part 1 to get
