Mechanics of Fluids

84 Fluid statics
✷
that is,
(a) ∴ tan(φ + θ) =
tan θ = ax
az + g =
tan φ + tan θ
1 − tan φ tan θ
20/ √ 17
(5/ √ = 0.440
17) + 9.81
0.25 + 0.440
= = 0.775
1 − 0.25 × 0.440
∴ c = 0.5 m × 0.775 = 0.3875 m
�
Then volume of oil left = 0.5 0.5 2 − 1
�
0.5 × 0.3875
2
= 0.765 m 3 = 76.5 L
(b) From eqn 2.26 p =−ϱaxx − ϱ(az + g)z + constant
Pressure at B is atmospheric and if B is at (0,0) then constant = 0
Point A will be at [(0.5 m) sin φ, −(0.5 m) cos φ]
∴ pA =−ϱa cos φ(0.5 m) sin φ + ϱ(a sin φ + g)(0.5 m) cos φ
PROBLEMS
= ϱg(0.5 m) cos φ = 880 kg · m −3 9.81 N · kg −1 0.5 m 4
√ 17
= 4190 Pa
2.1 To what head of carbon tetrachloride (relative density 1.59) is
a pressure of 200 kPa equivalent?
2.2 A tank 3.5 m long and 2.5 m wide contains alcohol of relative
density 0.82 to a depth of 3 m. A 50 mm diameter pipe leads
from the bottom of the tank. What will be the reading on a
gauge calibrated in Pa connected at a point (a) 150 mm above
the bottom of the tank; (b) in the 50 mm diameter pipe, 2 m
below the bottom of the tank; (c) at the upper end of a 25 mm
diameter pipe, connected to the 50 mm pipe 2 m below the
bottom of the tank, sloping upwards at 30 ◦ to the horizontal
for 1.2 m and then rising vertically for 600 mm? What is the
load on the bottom of the tank?
2.3 To what head of air (R = 287 J · kg −1 · K −1 ) at an absolute
pressure of 101.3 kPa and temperature of 15 ◦ C is a pressure
of 75 mm of water equivalent?
2.4 A spherical air bubble rises in water. At a depth of 9mits
diameter is 4 mm. What is its diameter just as it reaches the
free surface where the absolute pressure is 101.3 kPa? (Surface
tension effects are negligible.)
m 3