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
