fluid_mechanics

54 Chapter 2 ■ Fluid Statics
differences can be measured if the manometer fluid has nearly
the same specific weight as the flowing fluid. It is the difference
in the specific weights, 2 1 , that is important.
Hence, by rewriting the answer as h 2 1p A p B 21g 2 g 1 2
it is seen that even if the value of p A p B is small, the value of h 2
can be large enough to provide an accurate reading provided the
value of g 2 g 1 is also small.
p A – p B , kPa
3
2
1
(15.6 kN/m 3 , 2.90 kPa)
2 = 1
0
8
10 12 14 16
2 , kN/m3
F I G U R E E2.5b
2.6.3 Inclined-Tube Manometer
To measure small pressure changes, a manometer of the type shown in Fig. 2.12 is frequently used.
One leg of the manometer is inclined at an angle u, and the differential reading / 2 is measured
along the inclined tube. The difference in pressure p A p B can be expressed as
Inclined-tube
manometers can be
used to measure
small pressure differences
accurately.
2 ~ 1
sin θ
2
0 30 60 90
θ, deg
or
(2.15)
where it is to be noted the pressure difference between points 112 and 122 is due to the vertical distance
between the points, which can be expressed as / 2 sin u. Thus, for relatively small angles the
differential reading along the inclined tube can be made large even for small pressure differences.
The inclined-tube manometer is often used to measure small differences in gas pressures so that
if pipes A and B contain a gas then
or
p A g 1 h 1 g 2 / 2 sin u g 3 h 3 p B
p A p B g 2 / 2 sin u g 3 h 3 g 1 h 1
p A p B g 2 / 2 sin u
/ 2 p A p B
g 2 sin u
(2.16)
where the contributions of the gas columns h 1 and h 3 have been neglected. Equation 2.16 and the
figure in the margin show that the differential reading / 2 1for a given pressure difference2 of the inclined-tube
manometer can be increased over that obtained with a conventional U-tube manometer
by the factor 1sin u. Recall that sin u S 0 as u S 0.
γ 3
γ 1
B
A
(1)
h 3
(2)
γ 2
h 1 2
θ
F I G U R E 2.12
Inclined-tube manometer.