BENG1 INTRODUCTION to
THERMO-FLUIDS (THER 103)
TUTORIAL EXAMPLES in CONTINUITY
(SSL conditions are 101.325 kPa, and 15°C)
1.
A
100mm diameter pipeline divides into two pipes of 50mm diameter. Assuming the
flow rate also divides equally find the velocity ratio of the smaller to the
larger pipe. Find the diameter ratio if the velocity in all of the pipes is the
same. [2:1;
1.41:1]
2.
A
gas main is fed from three different sources. If the gas velocity in all
pipelines has to be limited to a mean velocity of 20 m/s, and the volume flow
rates from each of the three sources are 10 m³/s, 9 m³/s, and 20 m³/s
respectively, find the diameters of all of the pipelines. Explain how the
pipeline design might vary if the gas was fed:
(a) at a common junction, and (b) at intervals along the pipes.
[1.576 m;
0.798 m; 0.757 m; 1.128 m]
3.
An
air conditioning system provides air to three floors of a building through a
rectangular duct measuring 1m in width and 0.30 m in depth. Find the width of
the duct required if the air has to be distributed at the same inlet velocity
in the ratio 4:3:3 to each of the three floors where the depth of duct remains
the same. Assuming the air conditioning system was located on the roof of the
building what other factor has to be taken into account to ensure that the
correct air flows are delivered to each floor. [ 0.4 m; 0.3 m;
0.3 m]
4.
The
air velocity at the nozzle of a hot air gun is required to be 5 m/s through a
nozzle area of 8 cm2. If the air temperature at the nozzle is 120°C,
find the air mass flow. Find also the velocity of the air at inlet where the
inlet has an effective cross-sectional flow area of double the outlet area and
the inlet temperature is 22°C.
[0.00359 kg/s;
1.875 m/s]
5.
The fluid velocity profile across the diameter of a small bore tube with
laminar flow is given by a parabolic relationship, where the velocity at radius
r from the centre is given by 
where R is the radius of the tube, and vmax is the maximum fluid velocity (at
the centre of the tube).
Show that the average fluid velocity is half
the maximum velocity and occurs at a location at approximately 71% of the tube
radius. *