on . Posted in Fluid Dynamics

In Hazen-Williams coefficient, the hydraulic gradient is one of the parameters used in the equation to calculate the flow rate of water through a pipe.  The hydraulic grade, or hydraulic gradient, is a parameter in hydraulic engineering, as it helps determine the direction and rate of flow of water in a pipe or open channel.  It takes into account the elevation changes and head losses along the flow path.

$$m = ( v \;/\; C \; 1.318 \; r_h^{0.63} )^{1 / 0.54}$$     (Hazen-Williams Hydraulic Grade)

$$v = C \; 1.318 \; r_h^{0.63} \; m^{0.54}$$

$$C = v \;/\; 1.318 \; r_h^{0.63} \; m^{0.54}$$

$$r_h = ( v \;/\; C \; 1.318 \; m^{0.54} )^{1 / 0.63}$$

### Solve for m

 flow velocity, v Hazen-Williams coefficient, C hydraulic radius, rh

### Solve for rh

 flow velocity, v Hazen-Williams coefficient, C hydraulic grade line, m
Symbol English Metric
$$m$$ = hydraulic grade line slope $$dimensionless$$
$$v$$ = mean flow velocity $$ft \;/\; sec$$ $$m \;/\; s$$
$$C$$ = Hazen-Williams coefficient, see below for values $$dimensionless$$
$$r_h$$ = hydraulic radius $$ft$$ $$m$$

$$m = ( Q \;/\; C \; 0.285 \; d^{2.63} ) ^{1/0.54}$$     (Hazen-Williams Hydraulic Grade)

$$Q = C \; 0.285 \; d^{2.63} \; m^{0.54}$$

$$C = Q \;/\; 0.285 \; d^{2.63} \; m^{0.54}$$

$$d = ( Q \;/\; C \; 0.285 \; m^{0.54} ) ^{1/2.63}$$

### Solve for m

 flow rate, Q Hazen-Williams coefficient, C pipe inside diameter, d

### Solve for Q

 Hazen-Williams coefficient, C pipe inside diameter, d hydraulic grade line, m

### Solve for C

 flow rate, Q pipe inside diameter, d hydraulic grade line, m

### Solve for d

 flow rate, Q Hazen-Williams coefficient, C hydraulic grade line, m
Symbol English Metric
$$m$$ = hydraulic grade line slope $$dimensionless$$
$$Q$$ = flow rate $$ft^3 \;/\; sec$$ $$m^3 \;/\; s$$
$$C$$ = Hazen-Williams coefficient, see below for values $$dimensionless$$
$$d$$ = pipe inside diameter $$in$$ $$mm$$