The Delft Sand, Clay & Rock Cutting Model, 2019a

Exercises.
2 2
1 w c i
c g v h w 0.351.025 9.81 0.1 0.161
Fh
vc
k 0.00015
c
m
37.54 v 37.54 0.5 18.77
(kN)
The non-cavitational force does not depend on the water depth.
B: What are the horizontal cutting forces at 0 m, 15 m and 30 m water depths for the cavitational cutting
process?
h 1 w i
F d g z 10 h w 4.51.025 9.81 0.11 z 10
4.52 z 10
(kN)
This gives for 0 m water depth a force of 45.2 kN, for 15 m water depth a force of 113 kN and for 30 m water
depth a force of 180.8 kN.
C: At which velocities are the transitions between the cavitational and the non-cavitational cutting process
at 0 m, 15 m and 30 m water depths?
c
37.54 v 4.52 z 10 v 0.12 z 10 (m/sec)
c
This gives for 0 m water depth a transition velocity of 1.2 m/sec, for 15 m water depth a transition velocity of 3.0
m/sec and for 30 m water depth a transition velocity of 4.8 m/sec.
D: What is the specific energy at 0 m, 15 m and 30 m water depth at a cutting velocity of 1 m/s?
E
sp
Fh
vc Fh Fh
10
F
h w v h w 0.11
i c i
h
(kPa)
At a cutting velocity of 1 m/sec the cutting process is non-cavitational at all 3 water depths, so in all 3 cases the
specific energy is 375.4 kPa.
E: What is the specific energy at a water depth of 0 m, 15 m and 30 m at a cutting velocity of 2 m/s?
At a cutting velocity of 2 m/sec, the cutting process at 0 m water depth is cavitating, giving a specific energy of
452 kPa. At a water depth of 15 m the cutting process is non-cavitational giving a specific energy of 750.8 kPa.
At a water depth of 30 m the cutting process is also non-cavitational giving a specific energy of 750.8 kPa.
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