Page 323 - Fluid Mechanics and Thermodynamics of Turbomachinery

304 Fluid Mechanics, Thermodynamics of Turbomachinery
temperature of 25 ° C is 0.03166 bar. From the definition of NPSH, eqn. (9.24), we
obtain:
p a p v 5
H s D z D .1.013 0.03166/ ð 10 /.9810/ 2 D 8.003 m.
g
Thus, Thoma’s coefficient is, D H S /H E D 8.003/150 D 0.05336.
At the value of  SP D 0.8 given as data, the value of the critical Thoma coefficient
c corresponding to this is 0.09 from Figure 9.19. From the fact that < c , then
the turbine will cavitate.
From the definition of the suction specific speed

Q 1/2 44.9 ð 20 1/2
 SS D D D 200.8/26.375 D 7.613.
.gH S / 3/4 .9.81 ð 8.003/ 3/4
According to eqn. (1.12b), when  SS exceeds 4.0 (rad) then cavitation can occur,
giving further confirmation of the above conclusion.

Connection between Thoma’s coefficient, suction specific speed and
specific speed

The definitions of suction specific speed and specific speed are
Q 1/2 Q 1/2
 SS D and  S D
.gH S / 3/4 .gH E / 3/4
Combining and using eqn. (9.24), we get:
3/4
 S gH S 3/4
D D
 SS gH E
4/3

 S
∴ D . .9.26/
 SS
Exercise. Verify the value of Thoma’s coefficient in the earlier example using
the values of power specific speed, efficiency and suction specific speed given or
derived.
We use as data  SS D 7.613,  SP D 0.8 and H D 0.896 so that, from eqn. (1.9c),
p p
 S D  SP / H D 0.8/ 0.896 D 0.8452
∴ D .0.8452/7.613/ 4/3 D 0.05336.

Avoiding cavitation
By rearranging eqn. (9.24) and putting D c , a critical value of z can be derived
on the boundary curve between cavitation and no cavitation. Thus,
p a p v
z D z c D c H E D .101.3 3.17//9.81 0.09 ð 150 D3.5m.
g
This means that the turbine would need to be submerged at a depth of 3.5 m or
more below the surface of the tailwater and, for a Francis turbine, would lead to