Energy Losses

• Energy losses during the flow of fluid through a system occur due to various factors.
• Here are the main types of losses:

1. Frictional  Loss:

   • Occurs due to the friction between the fluid and the pipe walls.
   • Depends on the flow velocity, pipe diameter, fluid viscosity, and pipe roughness.
   • Calculated using the Darcy-Weisbach equation:

   • $h_f = f \cdot \frac{L}{D} \cdot \frac{v^2}{2g}$

     • • hf​ = head loss due to friction
       • f = friction factor
       • L = length of the pipe
       • D = diameter of the pipe
       • v = flow velocity
       • g = acceleration due to gravity

2. Enlargement Loss:

   • Occurs when the fluid flows from a smaller pipe to a larger pipe.
   • The sudden increase in cross-sectional area causes a drop in velocity and kinetic energy, resulting in energy loss.
   • Expressed as:

   • $h_e = K_e \cdot \frac{v_1^2}{2g}$

     • • he​ = head loss due to enlargement
       • Ke​ = loss coefficient for enlargement
       • v1​ = velocity in the smaller pipe

3. Constriction Loss:

   • Occurs when the fluid flows from a larger pipe to a smaller pipe.
   • The sudden decrease in cross-sectional area causes an increase in velocity, leading to turbulence and energy loss.
   • Expressed as:

   • $h_c = K_c \cdot \frac{v_2^2}{2g}$

     1. h_c​ = head loss due to constriction
     2. Kc​ = loss coefficient for constriction
     3. v2​ = velocity in the smaller pipe

4. Fitting Loss:

• Occurs due to the presence of fittings like elbows, tees, valves, and other components in the piping system.
• Each fitting introduces additional resistance and turbulence, causing energy loss.
• Expressed as:

• $h_{\text{fitting}} = K_f \cdot \frac{v^2}{2g}$

  • H_{fittings =} head loss due to fittings
  • Kf​ = loss coefficient for the fitting
  • v = flow velocity
• These losses collectively contribute to the overall energy loss in a fluid flow system, impacting the efficiency and performance of fluid transport.

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