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 \dfrac{L}{D}\dfrac{V^2}{2g}

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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 = \dfrac{V_1^2}{2g}+\dfrac{p_1}{\rho g} + z_1 =\dfrac{V_2^2}{2g}+\dfrac{p_2}{\rho g} + z_2

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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 \dfrac{L}{D} \dfrac{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 \dfrac{\epsilon}{D}. Click here to continue reading