# Blog Archives

## Closed Conduit Hydraulics – Friction and Minor Losses

Friction and minor losses are glossed over in the darcy-weisbach article but I want to throw in some extra notes here. Friction occurs over every bit of length of a close-conduit system and is usually a surprisingly high amount of energy loss. Friction depends on the material of the pipe and the velocity of flow. The formula for frictional head loss IS the Darcy-Weisbach equation.

$$h_f = f \frac{L}{D}\frac{V^2}{2g}$$

## Closed Conduit Hydraulics – Bernoulli Equation

The Bernoulli Equation is used to analyze flow in closed pipe systems and is one of the most used equations in hydraulics (that I can remember!).

The base form of the equation relates energy between two or more points in a system. I think it is easier to remember and use in terms of head loss(ft or m).

$$h_f = \frac{V_1^2}{2g}+\frac{p_1}{\rho g} + z_1 = \frac{V_2^2}{2g}+\frac{p_2}{\rho g} + z_2$$ Click here to continue reading

## Closed Conduit Hydraulics – Hazen Williams Equation

Hazen-Williams can be used to determine the flow characteristics in closed conduits (pipe systems).

### For Velocity

$$V = 1.318CR^{0.63}S^{0.54} \text{ (US)}$$

$$V = 0.849CR^{0.63}S^{0.54} \text{ (SI)}$$

S = slope, in decimal form. This is equivalent to $$h_f/L$$

R = hydraulic radius, $$\text{(Area of flow)}/\text{(wetted perimeter)}$$

C = Roughness Coefficient, get this from a table (available in both the AIO and CERM) Click here to continue reading

## Closed Conduit Hydraulics – Darcy-Weisbach Equation

The Darcy-Weisbach equation is used to determine flow characteristics in closed conduit systems (pipes). It is probably more common than the Hazen-Williams equation due to it being able to solve for systems in both laminar AND turbulent flow.

$$h_f = f \frac{L}{D} \frac{V^2}{2g}$$

• headloss $$h_f$$ (ft)
• friction factor $$f$$, length $$L$$
• length $$L$$ (ft)
• diameter $$D$$ (ft)
• velocity $$V$$ \frac{ft}{s}\)
• gravity g $$32.2 \frac{ft}{s^2}$$

#### Friction Factor

The friction factor $$f is either given or must be calculated using a Moody-Stanton diagram (available in both the AIO and CERM). Getting the friction factor from a Moody-Stanton chart requires the Reynolds Number \(Re$$, and relative roughness $$\frac{\epsilon}{D}$$. Click here to continue reading