Friction Loss in Pipe Flow: Darcy's Equation
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Questions and Answers

What does the symbol 'v' represent in Darcy's Equation?

  • Diameter of pipe
  • Length of straight pipe
  • Average velocity (correct)
  • Gravitational force

    • What is the unit of the friction factor 'f' in Darcy's Equation?

  • Meter per second
  • Dimensionless (correct)
  • Meter
  • Meter per second squared

    • What is the purpose of Moody's Chart?

  • To calculate the friction loss in pipes
  • To find the value of the friction factor (correct)
  • To determine the Reynolds number
  • To measure the surface imperfection of the pipe

    • What is the ratio of in Moody's Chart?

    <p>Surface imperfection to inner diameter</p> Signup and view all the answers

    What are the two parameters required to find the friction factor using Moody's Chart?

    <p>Reynolds number and relative roughness</p> Signup and view all the answers

    What is the unit of the friction loss 'hf' in Darcy's Equation?

    <p>Meter</p> Signup and view all the answers

    What is the purpose of Moody's chart?

    <p>To determine the friction factor for pipe flow</p> Signup and view all the answers

    What is the unit of dynamic viscosity of water?

    <p>Ns/m2</p> Signup and view all the answers

    What is the value of the dynamic viscosity of water given in the example?

    <p>1.49x10-3 Ns/m2</p> Signup and view all the answers

    What is the diameter of the cast iron pipe mentioned in the example?

    <p>30 cm</p> Signup and view all the answers

    What is the flow rate of water mentioned in the example?

    <p>200 L/s</p> Signup and view all the answers

    What is the purpose of finding the head loss per 100 m of pipe?

    <p>To design an efficient piping system</p> Signup and view all the answers

    What is the value of the diameter in meters?

    <p>0.3</p> Signup and view all the answers

    What is the value of the velocity in meters per second?

    <p>2.829</p> Signup and view all the answers

    What is the value of the Reynolds number?

    <p>5.70 × 10^5</p> Signup and view all the answers

    What is the value of the friction factor, f?

    <p>0.019</p> Signup and view all the answers

    What is the head loss, hf, in meters of water column per 100m of pipe length?

    <p>2.583</p> Signup and view all the answers

    What is the ratio of ε/d?

    <p>0.0008</p> Signup and view all the answers

    What is the relationship between the diameter and friction loss?

    <p>The smaller the diameter, the greater the friction loss.</p> Signup and view all the answers

    What is the value of the density of water, ρwater, in kg/m^3?

    <p>1000</p> Signup and view all the answers

    What is the formula to calculate the losses due to sudden enlargement?

    <p>hm = (1 - A2/A1) v^2 / (2g)</p> Signup and view all the answers

    What is the value of the coefficient of contraction (Cc) for a sudden contraction?

    <p>Cc = 0.62 + 0.38 (A2)^2</p> Signup and view all the answers

    What is the limitation on the ratio of A2 to A1 for the sudden contraction formula to be valid?

    <p>A2/A1 between 0.1 and 1</p> Signup and view all the answers

    What is the formula to calculate the losses due to sudden contraction?

    <p>hm = Kv^2 / (2g)</p> Signup and view all the answers

    What type of design issue can lead to significant losses?

    <p>Poorly designed inlet of a reservoir or a tank</p> Signup and view all the answers

    What is the term for the sudden change in pipe cross-sectional area?

    <p>Sudden contraction</p> Signup and view all the answers

    What is the total friction loss due to pipe and fittings in the given example?

    <p>17.25 m</p> Signup and view all the answers

    What is the formula for head loss due to friction along the pipe length?

    <p>hf = fLv^2 / (2gd)</p> Signup and view all the answers

    What is the value of the loss at pipe exit in the given example?

    <p>0.88 m</p> Signup and view all the answers

    What is the formula for head loss due to sudden enlargement?

    <p>hm = K(v1^2 - v2^2) / (2g)</p> Signup and view all the answers

    What is the total head loss in a pipeline with pipes connected in series?

    <p>The sum of frictional loss in each pipe plus local shock losses</p> Signup and view all the answers

    What is the formula for head loss due to sudden contraction?

    <p>hm = K(v1^2 - v2^2) / (2g)</p> Signup and view all the answers

    What is the purpose of finding the equivalent length of pipe fittings?

    <p>To add to the actual length of pipe for calculating frictional loss</p> Signup and view all the answers

    What is the value of the resistance coefficient K for a sudden entrance?

    <p>0.5</p> Signup and view all the answers

    What is the formula for head loss due to entrance?

    <p>hm = Kv^2 / (2g)</p> Signup and view all the answers

    What is the formula for head loss due to pipe fittings?

    <p>hf = KLv^2 / (2gd)</p> Signup and view all the answers

    Study Notes

    Friction Loss in Pipe Flow - Darcy's Equation

    • Darcy's Equation calculates friction losses in pipes: hf = f * L * v^2 / (2 * g * d)
    • hf is the friction loss (m), f is the friction factor (dimensionless), L is the length of straight pipe (m), d is the diameter of pipe (m), v is the average velocity (m/s), and g is the gravitational force (m/s2)

    Moody's Chart

    • Moody's Chart provides a value of friction factor, f, when Reynolds number (Re) and relative roughness of the pipe (ε/d) are known
    • Reynolds number (Re) is a dimensionless value that determines the nature of fluid flow
    • Relative roughness (ε/d) is the ratio of surface imperfection to inner diameter of the pipe

    Example 1: Friction Loss in a Cast Iron Pipe

    • Water flows in a 30 cm diameter cast iron pipe with relative roughness 0.0008
    • The water flow rate is 200 L/s, and the dynamic viscosity of water is 1.49x10-3 Ns/m2
    • The head loss per 100 m of pipe is calculated using Darcy's Equation and Moody's Chart

    Minor Energy Losses in Pipes

    • Minor energy losses occur due to sudden enlargement, sudden contraction, and entrance losses
    • Sudden enlargement losses: hm = (1 - A1/A2) * v^2 / (2 * g)
    • Sudden contraction losses: hm = K * v^2 / (2 * g), where K = (1 - A1/A2)^2
    • Entrance losses: hm = K * v^2 / (2 * g), where K = 0.5 for sudden entrance and K = 0.8 for protruded entrance

    Summary of Head Losses in Pipe Systems

    • Frictional head loss: hf = f * L * v^2 / (2 * g * d)
    • Sudden enlargement head loss: hm = (1 - A1/A2) * v^2 / (2 * g)
    • Sudden contraction head loss: hm = K * v^2 / (2 * g), where K = (1 - A1/A2)^2
    • Entrance head loss: hm = K * v^2 / (2 * g), where K = 0.5 for sudden entrance and K = 0.8 for protruded entrance
    • Pipe fittings head loss: determine equivalent length, L, from L/d ratio and add to actual length of pipe

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    Description

    Learn about Darcy's Equation for calculating friction losses in pipes and Moody's Chart for determining friction factor. Quiz covers pipe flow, friction loss, and fluid dynamics.

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