Calculations and Pipe Notes

Calculations and Equations

  • Given equation: V<em>1V</em>2=π\frac{V<em>1}{V</em>2} = \pi
  • Relationship between variables: DV<em>1=DV</em>2DV<em>1 = DV</em>2
  • Initial equation: D<em>1V</em>1=D<em>2V</em>2D<em>1 \sqrt{V</em>1} = D<em>2 \sqrt{V</em>2}
  • Taking the square root of both sides leads to: D<em>12V</em>1V<em>2=D</em>1\sqrt{D<em>1^2 \frac{V</em>1}{V<em>2}} = D</em>1
  • Which simplifies to: D<em>2=D</em>1V<em>1V</em>2D<em>2 = D</em>1 \sqrt{\frac{V<em>1}{V</em>2}}
  • Given values: V<em>1V</em>2=0.01\frac{V<em>1}{V</em>2} = 0.01
  • Calculating D2D_2:
    • D2=0.01×21D_2 = 0.01 \times \sqrt{21}
  • Result: D2=0.002 mD_2 = 0.002 \text{ m}
  • Converting meters to centimeters:
    • D2=0.002×100 cmD_2 = 0.002 \times 100 \text{ cm}
  • Final result in centimeters: D2=0.2 cmD_2 = 0.2 \text{ cm}

Pipe at Lower End

  • Reference to section 6.3: The pipe near the lower end.