# Curvature Coefficient

on . Posted in Geotechnical Engineering

Curvature coefficient, abbreviated as $$C_c$$, also called coefficient of curvature, a dimensionless number, classifies a soil as well graded or poorly graded.  It is a measure of the fineness or coarseness of the soil particles.

Particle size distribution curves are commonly used in geotechnical engineering to describe the distribution of different sizes of particles in a soil sample.  These curves provide information about the proportion of various particle sizes within the soil.

### Curvature coefficient categorizes fluids into different regimes

• Mildly Curved Flow (C < 1)  -  The curvature effects are relatively small, and the flow behaves similarly to that in a straight channel.
• Moderately Curved Flow (1 < C < 100)  -  The curvature starts to significantly influence the flow patterns, leading to secondary flow structures.
• Strongly Curved Flow (C > 100)  -  The curvature dominates the flow behavior, and the secondary flow patterns become even more pronounced.

Understanding the curvature coefficient is important for predicting flow patterns, pressure distribution, and other characteristics in curved channels.  It's particularly relevant in areas such as river hydraulics, pipeline design, and understanding the behavior of flows in bends or turns.

## Curvature Coefficient formula

$$\large{ C_c = \frac{ D_{30}^2 }{ D_{60} \; D_{10} } }$$     (Curvature Coefficient)

$$\large{ D_{30} = \sqrt{ D_{60} \; D_{10} } }$$

$$\large{ D_{60} = \frac{ D_{30}^2 }{ C_c \; D_{10} } }$$

$$\large{ D_{10} = \frac{ D_{30}^2 }{ C_c \; D_{60} } }$$

### Solve for Cc

 30% sieve diameter, D30 60% sieve diameter, D60 10% sieve diameter, D10

### Solve for D30

 60% sieve diameter, D60 10% sieve diameter, D10

### Solve for D60

 30% sieve diameter, D30 curvature coefficient, Cc 10% sieve diameter, D10

### Solve for D10

 30% sieve diameter, D30 curvature coefficient, Cc 60% sieve diameter, D60

Symbol English Metric
$$\large{ C_c }$$ = curvature coefficient $$\large{dimensionless}$$
$$\large{ D_{30} }$$ = is the sieve diameter (grain size) which there are 30% of particles go through. $$\large{in}$$ $$\large{mm}$$
$$\large{ D_{60} }$$ = is the sieve diameter (grain size) which there are 60% of particles go through. $$\large{in}$$ $$\large{mm}$$
$$\large{ D_{10} }$$ = is the sieve diameter (grain size) which there are 10% of particles go through. $$\large{in}$$ $$\large{mm}$$ 