# Wetted Perimeter

on . Posted in Fluid Dynamics

Wetting perimeter, abbreviated as $$P_w$$, is a hydraulic parameter used to describe the contact length between the fluid and the boundary of an open channel or pipe.  It is the total length of the surface of the channel or pipe that is in contact with the fluid.   The wetted perimeter depends on the shape and size of the channel or pipe and the water level.

### Wetted Perimeter Index

For example, in a rectangular channel, the wetted perimeter is the sum of the length of the bottom and the two sides of the channel that are in contact with the fluid.  In a circular pipe, the wetted perimeter is the circumference of the pipe

The wetted perimeter is an important parameter in the calculation of hydraulic variables, such as flow rate, velocity, and hydraulic depth, in open channel and pipe flow systems.

### Wetting perimeter of a circular pipe formula

$$P_w = ( cos^{-1} ( 1 - ( h \;/\; r ) \;) \;) \; d$$     (Wetted Perimeter of a Circular Pipe)

$$h = r \; ( 1 - ( cos\; ( P_w \;/\; d )\;) \; )$$

$$r = 1 - (cos \;( P_w \;/\; d ) \; ) \;/\; h$$

$$d = P_w \;/\; cos \; ( 1 - ( h \;/\; r ) \;)$$

### Solve for Pw

 fluid depth, h inside radius, r outside diameter, d

### Solve for h

 inside radius, r wetting perimeter, Pw outside diameter, d

### Solve for r

 wetting perimeter, Pw outside diameter, d fluid depth, h

### Solve for d

 wetting perimeter, Pw fluid depth, h inside radius, r

Symbol English Metric
$$P_w$$ = wetting perimeter $$in$$ $$mm$$
$$h$$ = fluid depth $$in$$ $$mm$$
$$r$$ = inside radius $$in$$ $$mm$$
$$d$$ = outside diameter $$in$$ $$mm$$

### Wetting perimeter of a Rectangular Channel formula

$$P_w = b + 2 \; h$$     (Wetted Perimeter of a Rectangular Channel)

$$b = Pw - 2 \; h$$

$$h = Pw - b \;/\; 2$$

### Solve for Pw

 bottom width, b fluid height, h

### Solve for b

 wetting perimeter, Pw fluid height, h

### Solve for h

 wetting perimeter, Pw bottom width, b

Symbol English Metric
$$P_w$$ = wetting perimeter $$ft$$ $$m$$
$$b$$ = bottom width $$ft$$ $$m$$
$$h$$ = fluid depth $$ft$$ $$m$$

### Wetting perimeter of a Trapezoidal Channel formula

$$P_w = b + 2 \; ( \; ( t - b \;/\; 2 )^2 + h^2 )^\frac{1}{2}$$
Symbol English Metric
$$P_w$$ = wetting perimeter $$ft$$ $$m$$
$$b$$ = bottom width of liquid $$ft$$ $$m$$
$$t$$ = top width of liquid $$ft$$ $$m$$
$$h$$ = fluid depth $$ft$$ $$m$$

### Wetting perimeter of a Triangle Channel formula

$$P_w = 2 \; h \; \left( 1 + z^2 \right)^\frac{1}{2}$$
Symbol English Metric
$$P_w$$ = wetting perimeter $$ft$$ $$m$$
$$h$$ = fluid depth $$ft$$ $$m$$
$$z$$ = horiz. side slope $$ft$$ $$m$$