GATE CE 2018 Set 1 — Question 49
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.NAT+2 / -0MediumEuler MethodNumerical Integration & ODEsEngineering MathematicsGradually Varied FlowHydraulic Jump & Varied FlowWater Resources Engineering
Engineering Mathematics → Hydraulic Jump & Varied Flow → Euler Method
Last updated
Question
Variation of water depth () in a gradually varied open channel flow is given by the first order differential equationGiven initial condition: . The depth (in m, up to three decimal places) of flow at a downstream section at from one calculation step of Single Step Euler Method is ______
Correct answer
0.78 to 0.8
Solution
The Single Step Euler Method for solving a first-order differential equation with initial condition and step size is given by:
Given:
Initial condition:
Target point:
Step size: Calculate the value of the function at the initial point:
Using the property :
Substituting these values:
Now, apply the Euler's formula:
Rounding to three decimal places, the depth is .
The official answer range is to .
Given:
Initial condition:
Target point:
Step size: Calculate the value of the function at the initial point:
Using the property :
Substituting these values:
Now, apply the Euler's formula:
Rounding to three decimal places, the depth is .
The official answer range is to .
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.