Mechanics of Fluids

292 Flow and losses in pipes and fittings
Fig. 7.28
is rotated about its axis until the stagnation point S is mid-way between
P1 and P2: the pressures at P1 and P2 are then equal as indicated by a null
reading on the manometer. The flow direction is then the bisector of the angle
P1OP2. According to inviscid flow theory, the pressure recorded at P1 or
P2 would be the static pressure of the undisturbed stream if P1 and P2 were
each 30◦ from S (from eqn 9.27). Frictional effects, however, make the angle
θ about 39 1 ◦
4 in practice. Thus if the angle P1OP2 is 78 1 ◦
2 the instrument
may be used also to measure static pressure and, when turned through 39 1 ◦
,
the stagnation pressure. The angles are larger when compressibility effects
become significant. In other designs small Pitot tubes are used in place of
pressure tappings on a cylinder.
For three-dimensional flow a sphere may be employed in place of the cylinder:
three pressure tappings are then situated at the vertices of an equilateral
triangle, and the pressures at all three points are equal when the flow is
parallel to the radius to the centroid of the triangle.
The hot-wire anemometer can be adapted as a yaw meter for twodimensional
flow by incorporating two similar wires placed in the plane of
flow at an angle to each other. A position is found in which the heat losses
from the wires are equal; the flow direction is then that which bisects the
angle between the wires. For three-dimensional flow three wires are required,
arranged as adjoining edges of a regular tetrahedron.
PROBLEMS
7.1 Calculate the power required to pump sulphuric acid (dynamic
viscosity 0.04 Pa · s, relative density 1.83) at 45 L · s −1 from a
supply tank through a glass-lined 150 mm diameter pipe, 18 m
long, into a storage tank. The liquid level in the storage tank is
6 m above that in the supply tank. For laminar flow f = 16/Re;
for turbulent flow f = 0.0014(1 + 100Re −1/3 ) if Re < 10 7 .
Take all losses into account.
7.2 In a heat exchanger there are 200 tubes each 3.65 m long and
30 mm outside diameter and 25 mm bore. They are arranged
axially in a cylinder of 750 mm diameter and are equally spaced
from one another. A liquid of relative density 0.9 flows at a
mean velocity of 2.5 m · s −1 through the tubes and water flows
at 2.5 m · s −1 between the tubes in the opposite direction. For
all surfaces f may be taken as 0.01. Neglecting entry and exit
4