**
****The Hydraulic Gradient
versus the Line Speed**

**The hydraulic gradient equals
the pressure gradient divided by the density of the carrier liquid and the
gravitational constant. The pressure gradient is the pressure required to pump a
mixture over a certain length of pipeline divided by this
length.**

**So: i=Δp/(ρ**_{l}·g·ΔL)
and Δp=i·(ρ_{l}·g·ΔL)

**The advantage of the hydraulic
gradient versus the line speed graph is that it relates directly to dredging
practice and can easily be combined with pump curves in order to determine the
working point of a pump/pipeline system. The disadvantage is that it depends
strongly on the volumetric concentration C**_{vs} or
C_{vt} and the relative submerged density R_{sd}, so for
different concentrations and/or relative submerged densities different graphs
have to be made.

**Two graphs are shown, first
the graph for constant spatial volumetric concentration curves (often laboratory
conditions) and second a graph for constant transport volumetric
concentration curves (dredging practice).**

**Constant Spatial Volumetric
Concentration Curves**

**The basic DHLLDV Framework is
based on constant spatial volumetric concentration and consists of 4 main flow
regimes, which may be subdivided into a larger set of sub-regimes. The regimes
are the fixed bed regime (FB) without or with sheet flow, the sliding bed regime
(SB), the heterogeneous regime (He) and the homogeneous regime (Ho). Only at
high particle diameter to pipe diameter ratios (>0.015) a
5**^{th} regime may occur, the sliding flow regime
(SF).

**Constant Transport Volumetric
Concentration Curves**

**The constant transport
volumetric concentration curves are derived from the constant spatial
concentration curves and a holdup function or slip factor relation. This
holdup function depends strongly on the Limit Deposit
Velocity.**

**The Relative Excess
Hydraulic Gradient versus the Line Speed**

**The relative excess
hydraulic gradient E**_{rhg} equals the difference between the mixture
hydraulic gradient i_{m} and the liquid hydraulic gradient
i_{l} divided by the volumetric concentration C_{vs} or
C_{vt} and the relative submerged density
R_{sd}.

**So:
E**_{rhg}=(i_{m}-i_{l})/(C_{vs}·R_{sd})

**The advantage of using the
relative excess hydraulic gradients is that for the constant spatial volumetric
concentration case this parameter is almost independent of parameters like the
concentration and the relative submerged density. However for the constant
transport volumetric concentration case it depends strongly on the concentration
below the Limit Deposit Velocity. **

**The advantage of plotting
this parameter versus the line speed is that the value can be related to
dredging practice where the line speed is a known.**

**Two graphs are shown, first
the graph for constant spatial volumetric concentration curves (often laboratory
conditions) and second a graph for constant transport volumetric
concentration curves (dredging practice).**

**Constant Spatial Volumetric
Concentration Curves**

**The basic DHLLDV Framework is
based on constant spatial volumetric concentration and consists of 4 main flow
regimes, which may be subdivided into a larger set of sub-regimes. The regimes
are the fixed bed regime (FB) without or with sheet flow, the sliding bed regime
(SB), the heterogeneous regime (He) and the homogeneous regime (Ho). Only at
high particle diameter to pipe diameter ratios (>0.015) a 5**^{th}
regime may occur, the sliding flow regime (SF).

**Constant Transport Volumetric
Concentration Curves**

**The constant transport
volumetric concentration curves are derived from the constant spatial
concentration curves and a holdup function or slip factor relation. This
holdup function depends strongly on the Limit Deposit
Velocity.**

**The Relative Excess
Hydraulic Gradient versus the Hydraulic Gradient**

**The relative excess
hydraulic gradient E**_{rhg} equals the difference between the mixture
hydraulic gradient i_{m} and the liquid hydraulic gradient
i_{l} divided by the volumetric concentration C_{vs} or
C_{vt} and the relative submerged density
R_{sd}.

**So:
E**_{rhg}=(i_{m}-i_{l})/(C_{vs}·R_{sd})

**The advantage of using the
relative excess hydraulic gradients is that for the constant spatial volumetric
concentration case this parameter is almost independent of parameters like the
concentration and the relative submerged density. However for the constant
transport volumetric concentration case it depends strongly on the concentration
below the limit deposit velocity. **

**The advantage of plotting
this parameter versus the hydraulic gradient of the liquid makes the graph
almost dimensionless.**

**Two graphs are shown, first
the graph for constant spatial volumetric concentration curves (often laboratory
conditions) and second a graph for constant transport volumetric
concentration curves (dredging practice).**

**Constant Spatial Volumetric
Concentration Curves**

**The basic DHLLDV model is
based on constant spatial volumetric concentration and consists of 4 main flow
regimes, which may be subdivided into a larger set of sub-regimes. The regimes
are the fixed bed regime (FB) without or with sheet flow, the sliding bed regime
(SB), the heterogeneous regime (He) and the homogeneous regime (Ho). Only at
high particle diameter to pipe diameter ratios (>0.015) a 5**^{th}
regime may occur, the sliding flow regime (SF).

**Constant Transport Volumetric
Concentration Curves**

**The constant transport
volumetric concentration curves are derived from the constant spatial
concentration curves and a holdup function or slip factor relation. This
holdup function depends strongly on the Limit Deposit
Velocity.**