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In a triangular notch, there is an error of 6% in observing the head. The error in the computed discharge is
- a)10%
- b)6%
- c)12%
- d)15%
Correct answer is option 'D'. Can you explain this answer?
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In a triangular notch, there is an error of 6% in observing the head. ...
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In a triangular notch, there is an error of 6% in observing the head. ...
Explanation:
The discharge through a triangular notch is given by the formula:
Q = C d2/3 * L * H1/2
where,
Q = Discharge
Cd = Coefficient of discharge
L = Length of the notch
H = Head on the notch
Error in observing the head:
The error in observing the head is given as 6%.
So, the observed head will be:
Observed Head = Actual Head + Error in Head
Let the actual head be H and the observed head be H'.
So, H' = H + 6% of H = 1.06H
Error in computed discharge:
The formula for the discharge through a triangular notch involves the term H1/2.
So, the computed discharge with the observed head will be:
Q' = C d2/3 * L * H'1/2
Substituting the value of H', we get:
Q' = C d2/3 * L * (1.06H)1/2
Q' = C d2/3 * L * 1.03H
The error in computed discharge will be:
Error in computed discharge = ((Computed discharge - Actual discharge)/Actual discharge) * 100
Let the actual discharge be Q and the error in computed discharge be E.
So, E = ((Q' - Q)/Q) * 100
Substituting the value of Q' and simplifying, we get:
E = ((C d2/3 * L * 1.03H - C d2/3 * L * H)/ (C d2/3 * L * H)) * 100
E = 3%
Therefore, the error in computed discharge is 3% which is option D.
The discharge through a triangular notch is given by the formula:
Q = C d2/3 * L * H1/2
where,
Q = Discharge
Cd = Coefficient of discharge
L = Length of the notch
H = Head on the notch
Error in observing the head:
The error in observing the head is given as 6%.
So, the observed head will be:
Observed Head = Actual Head + Error in Head
Let the actual head be H and the observed head be H'.
So, H' = H + 6% of H = 1.06H
Error in computed discharge:
The formula for the discharge through a triangular notch involves the term H1/2.
So, the computed discharge with the observed head will be:
Q' = C d2/3 * L * H'1/2
Substituting the value of H', we get:
Q' = C d2/3 * L * (1.06H)1/2
Q' = C d2/3 * L * 1.03H
The error in computed discharge will be:
Error in computed discharge = ((Computed discharge - Actual discharge)/Actual discharge) * 100
Let the actual discharge be Q and the error in computed discharge be E.
So, E = ((Q' - Q)/Q) * 100
Substituting the value of Q' and simplifying, we get:
E = ((C d2/3 * L * 1.03H - C d2/3 * L * H)/ (C d2/3 * L * H)) * 100
E = 3%
Therefore, the error in computed discharge is 3% which is option D.
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