Question:
An error of 1 % in measuring head (H) will produce
An error of 1 % in measuring head (H) will produce
Show Hint
The percentage error in discharge is simply the exponent of the head \(H\) multiplied by the percentage error in the head measurement.
Since the exponent for a triangular weir is 2.5 and for a rectangular weir is 1.5, the triangular weir will always exhibit a higher percentage error.
Since the exponent for a triangular weir is 2.5 and for a rectangular weir is 1.5, the triangular weir will always exhibit a higher percentage error.
Updated On: Jul 7, 2026
- Same error in discharge over a rectangular weir and triangular weir
- More error in discharge over triangular weir compared to rectangular weir
- More error in discharge over rectangular weir compared to triangular weir
- No error in discharge over a rectangular weir and triangular weir
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Step 1: Understanding the Concept:
Discharge over weirs depends on the measured head of the water flowing over them.
An error in measuring the head propagates to the calculated discharge based on the power relation between discharge and head.
Step 2: Key Formula or Approach:
For a rectangular weir, the discharge \(Q_r\) is given by:
\[ Q_r \propto H^{3/2} \] For a triangular weir (V-notch), the discharge \(Q_t\) is given by:
\[ Q_t \propto H^{5/2} \]
Step 3: Detailed Explanation:
Let us use differential approximation to calculate the relative error in discharge for both cases:
For the rectangular weir:
\[ \ln(Q_r) = \frac{3}{2} \ln(H) + \text{constant} \] Differentiating both sides:
\[ \frac{dQ_r}{Q_r} = 1.5 \frac{dH}{H} \] Thus, a 1 % error in measuring head (\(\frac{dH}{H} = 1\%\)) produces a 1.5 % error in the calculated rectangular weir discharge.
For the triangular weir:
\[ \ln(Q_t) = \frac{5}{2} \ln(H) + \text{constant} \] Differentiating both sides:
\[ \frac{dQ_t}{Q_t} = 2.5 \frac{dH}{H} \] Thus, a 1 % error in measuring head (\(\frac{dH}{H} = 1\%\)) produces a 2.5 % error in the calculated triangular weir discharge.
Comparing the two, the error in the discharge of a triangular weir (2.5 %) is higher than that of a rectangular weir (1.5 %).
Step 4: Final Answer:
The correct option is 2, which corresponds to "More error in discharge over triangular weir compared to rectangular weir".
Discharge over weirs depends on the measured head of the water flowing over them.
An error in measuring the head propagates to the calculated discharge based on the power relation between discharge and head.
Step 2: Key Formula or Approach:
For a rectangular weir, the discharge \(Q_r\) is given by:
\[ Q_r \propto H^{3/2} \] For a triangular weir (V-notch), the discharge \(Q_t\) is given by:
\[ Q_t \propto H^{5/2} \]
Step 3: Detailed Explanation:
Let us use differential approximation to calculate the relative error in discharge for both cases:
For the rectangular weir:
\[ \ln(Q_r) = \frac{3}{2} \ln(H) + \text{constant} \] Differentiating both sides:
\[ \frac{dQ_r}{Q_r} = 1.5 \frac{dH}{H} \] Thus, a 1 % error in measuring head (\(\frac{dH}{H} = 1\%\)) produces a 1.5 % error in the calculated rectangular weir discharge.
For the triangular weir:
\[ \ln(Q_t) = \frac{5}{2} \ln(H) + \text{constant} \] Differentiating both sides:
\[ \frac{dQ_t}{Q_t} = 2.5 \frac{dH}{H} \] Thus, a 1 % error in measuring head (\(\frac{dH}{H} = 1\%\)) produces a 2.5 % error in the calculated triangular weir discharge.
Comparing the two, the error in the discharge of a triangular weir (2.5 %) is higher than that of a rectangular weir (1.5 %).
Step 4: Final Answer:
The correct option is 2, which corresponds to "More error in discharge over triangular weir compared to rectangular weir".
Was this answer helpful?
0
0
Top ICAR AIEEA Agricultural Engineering and Technology Questions
- Which of the following farm equipment is not going to be utilized during the wheat production?
- On the farm, during paddy land preparation, if one wheel of tractor gets in mud, which of the following mechanism will be useful to take out the tractor from mud by distributing equal amount of traction at both the rear wheels?
- 20 labors engaged in a farm-operation on paddy farm for 6h. In an ideal conditions, how much maximum energy is utilized by labors into the farm?
(A) 8.94 kWh (B) 120 kWh (C) 12 hPh (D) 240 hPh Choose the correct answer from the options given below: - Which of the following farm operations utilizes the stationary source of power?
(A) Irrigation Water Lifting (B) Winnowing (C) Threshing (D) Harvesting (E) Cultivation (F) Transportation Choose the correct answer from the options given below: - Which of the following methods are employed for the estimation of infiltration characteristics of soil for design of irrigation system?
(A) Use of Infiltrometer (B) Measurement of subsidence of free water in a large basin (C) Estimation of accumulated infiltration from water front advance data Choose the correct answer from the options given below:
View More Questions
Top ICAR AIEEA Runoff Measurement Structures Questions
- (A) H-flumes are well suited for runoff measurement as they have a high capacity and are accurate at different rates of flow.
(B) They are also well suited where sediment sampling of the runoff is done using automatic silt samplers.
(C) The H-flume is useful for flows ranging from 0.009 to 0.85 cumec.
(D) For smaller and greater flows the dimensions of the H-flume are modified and are known as HS flumes for smaller flows and HL flumes for larger flows.
(E) H-flumes need not require calibration and the rating tables are to be used for measuring discharges.
Choose the correct answer from the options given below: - Which of the following statements regarding construction and installation of weirs are true?
(A). The velocity of approach of water to the weir should not be considered.
(B). Weir crest should be placed closer than 2H from the bottom of the channel.
(C). The head over the weir should be measured on the upstream side at a distance of at least 4 times the head of flow from the weir.
(D). The falling water surface from the weir should not have free flow.
Choose the correct answer from the options given below: - Which of the following statements regarding basic equation for flow through the weir are correct?
(A). \(Q = 0.0186 L H^{2/3}\)
(B). \(Q = 0.0184 L H^{7/2}\)
(C). \(Q = C L H^m\)
Choose the correct answer from the options given below: - Resistance to uniform turbulent flow in an open channel system is often expressed in terms of the resistance co-efficient using
A. Manning’s equation
B. Chezy’s equation
C. Darcy -Weisbach equation
D. Bernoulli’s equation
E. Francis Formula
Choose the correct answer from the options given below: - Given below are two statements
Statement I: Free board is the additional height of the dam provided as a safety factor to prevent overtopping due to unexpected runoff or by wave action.
Statement II: Free board is the vertical distance between the designed water elevation and the elevation of the top of the dam before settlement.
In light of the above statements, choose the most appropriate answer from the options given below
View More Questions
Top ICAR AIEEA Questions
- Which of the following statements is false?
- Which of the following is an example of an inventory?
- According to Adam Smith, productivity gains could be brought about through .
- The supply curve for an artificially scarce good is .
- Which of the following would not be considered an opportunity cost of paid employment?
View More Questions