GATE CE 2025 Set 2 — Question 60
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.NAT+2 / -0HardHydrostatic ForcesFluid Properties & StaticsWater Resources Engineering
Water Resources Engineering → Fluid Properties & Statics → Hydrostatic Forces
Last updated
Question
The shaft of a 6 m wide gate in the figure will fail at a moment of 3924 kN.m about the hinge P. The maximum value of water depth (in m) that the gate can hold is ________________ (round off to the nearest integer).Note:
Density of water = 1000 kg/m
Acceleration due to gravity = 9.81 m/s
Density of water = 1000 kg/m
Acceleration due to gravity = 9.81 m/s
Correct answer
7 to 9
Solution
Given:
Width of gate, m
Failure moment about hinge P, kN.m = N.m
Density of water, kg/m
Acceleration due to gravity, m/sFrom the figure, the gate is inclined with a vertical height of 4 m and a horizontal width of 3 m.
Length of the inclined gate, m.
Let be the angle of the gate with the horizontal. .Let be the depth of water to the hinge P (at the bottom of the gate).
The depth of any element at a distance from the hinge P is .The hydrostatic force on the element is:
The moment of this force about hinge P is:
Integrating from to m:
Setting N.m:
mRounding to the nearest integer, .
Width of gate, m
Failure moment about hinge P, kN.m = N.m
Density of water, kg/m
Acceleration due to gravity, m/sFrom the figure, the gate is inclined with a vertical height of 4 m and a horizontal width of 3 m.
Length of the inclined gate, m.
Let be the angle of the gate with the horizontal. .Let be the depth of water to the hinge P (at the bottom of the gate).
The depth of any element at a distance from the hinge P is .The hydrostatic force on the element is:
The moment of this force about hinge P is:
Integrating from to m:
Setting N.m:
mRounding to the nearest integer, .
Continue learning with Success Tracker
A step still unclear? Work through it with support
Use Success Tracker to ask about the reasoning, then try another GATE CE question to check your understanding.
AI-powered practice· Unlimited practice on eligible plans
- PYQs with solutions
- Attempt available previous-year questions, then compare your reasoning with the worked solution. Coverage varies by stream.
- Practice that adapts
- Choose a topic, work on weaker areas and bookmark questions to revisit. Your attempts feed your progress tracking.
- AI doubt support
- Ask follow-up questions about a step or concept while practising, instead of stopping at the final answer.
Unlimited practice is available on eligible plans. Free practice and AI usage have limits; check the current plan allowances before choosing.
This page stays readable without an account. AI responses can be wrong; check them against the solution and source material.
More questions on Fluid Properties & Statics
2026 Set 1 Q16Two reservoirs having different water levels are connected by two long parallel pipelines of same…2026 Set 1 Q17An irrigation canal is to be designed to deliver 10 cumec to meet the peak demand of 7500 hectare…2026 Set 2 Q19The Culturable Command Area (CCA) for a canal is 10000 hectares. The base period for a crop in the…2026 Set 2 Q20Following statements are made with respect to the mass curve of rainfall: (I) Slope at a point on…2026 Set 1 Q23Gradually Varied Flow (GVF) profiles in open channels given in Column 1 are to be matched with the…