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An error of 1% in measuring head over the apex of the notch (H) will produce an error of __________ in discharge over a triangular notch.
  • a)
    1%
  • b)
    1.5%
  • c)
    2%
  • d)
    2.5%
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
An error of 1% in measuring head over the apex of the notch (H) will p...
Calculation of Error in Discharge over a Triangular Notch

Head over the apex of the notch (H) is measured to calculate the discharge over a triangular notch. An error of 1% in measuring H will result in an error in discharge over the notch. Let's calculate the error in discharge.

Given:

Error in measuring H = 1%

Formula:

Discharge over the triangular notch is given by Q = 1.84/1000 x H^(3/2)

Differentiating the formula with respect to H, we get:

dQ/dH = 1.38/1000 x H^(1/2)

Now, let's calculate the error in discharge:

Error in Q = dQ/dH x Error in H

= 1.38/1000 x H^(1/2) x 1%

= 0.0138 x H^(1/2) %

As we know, the value of H is in cm, and the value of Q is in cubic meters per second (m^3/s). Therefore, we need to convert the value of H into meters (m).

Let's assume H = 10 cm = 0.1 m

Substituting the value of H in the formula, we get:

Error in Q = 0.0138 x (0.1)^(1/2) %

= 0.0138 x 0.316 %

= 0.00436 %

Therefore, an error of 1% in measuring H will produce an error of 0.00436% in discharge over a triangular notch.

Conclusion:

Hence, the correct option is D) 2.5% which is the closest option to the calculated error in discharge over a triangular notch.
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Community Answer
An error of 1% in measuring head over the apex of the notch (H) will p...
DQ/Q=2.5dh/h
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An error of 1% in measuring head over the apex of the notch (H) will produce an error of __________ in discharge over a triangular notch.a)1%b)1.5%c)2%d)2.5%Correct answer is option 'D'. Can you explain this answer?
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