Specific energy tells us how much energy water has in an open channel, measured from the channel bottom. In civil engineering, plotting a specific-energy diagram helps you see if a water flow is fast or slow.
Here is how to calculate and plot this diagram for a rectangular canal. 1. Understand the Formula The total specific energy (
) equals the water depth plus the velocity head. For a rectangular canal, we use this formula:
E=y+q22gy2cap E equals y plus the fraction with numerator q squared and denominator 2 g y squared end-fraction Here is what the letters mean: is the specific energy (in feet or meters). is the water depth (in feet or meters).
is the flow rate per unit width. You find it by dividing total flow ( ) by canal width ( is the acceleration due to gravity ( 2. Find Critical Depth The critical depth (
) is the depth where specific energy is at its absolute lowest. You must find this point first to structure your diagram correctly. Calculate it using this equation:
yc=q2g3y sub c equals the cube root of the fraction with numerator q squared and denominator g end-fraction end-root 3. Calculate Energy Values To plot the curve, choose a wide range of water depths ( ). Pick several numbers smaller than and several numbers larger than
Plug each depth into the main energy equation to find its matching Potential Energy ( Kinetic Energy (
q22gy2the fraction with numerator q squared and denominator 2 g y squared end-fraction Total Energy ( Very Large Critical ( Minimum Energy ( Emincap E sub m i n end-sub ) Very Small 4. Plot the Diagram Put specific energy ( ) on the horizontal x-axis. Put water depth ( ) on the vertical y-axis. Draw a straight, diagonal line where . This is your 45∘45 raised to the composed with power reference line. Now, plot your calculated
points. Connect them to form a smooth, C-shaped curve. The curve will approach your diagonal line as depth increases. 5. Read the Results
The final curve splits your flow options into two main zones: Subcritical Flow: The top half of the curve ( ). Water is deep and moves slowly. Supercritical Flow: The bottom half of the curve ( ). Water is shallow and moves fast. Alternate Depths: For any energy level higher than Emincap E sub m i n end-sub
, a vertical line will cross the curve at two points. These two depths share the exact same amount of energy. ✅ Conclusion
Calculating and plotting a specific-energy diagram lets engineers predict how water will behave in a rectangular channel. By finding the critical depth and plotting the energy curve, you can easily determine if a flow is subcritical or supercritical. If you want to build a specific chart, tell me: Your total flow rate or flow per unit width The width of your canal The unit system you prefer (metric or English) I can calculate the exact coordinates for your curve!
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