GATE Exam  >  GATE Questions  >  A horizontal pipe is feeding water into a res... Start Learning for Free
A horizontal pipe is feeding water into a reservoir from the top with a time-dependent volumetric flow-rate, Q (m3/h)= 1+0.1 x t where t is time in hours. The area of the base of the reservoir is 0.5 m2. Assuming that initially the reservoir was empty, the height of the water level in the reservoir after 60 minutes is __________ m.
    Correct answer is between '2.09,2.11'. Can you explain this answer?
    Most Upvoted Answer
    A horizontal pipe is feeding water into a reservoir from the top with ...
    Calculation of Water Level in Reservoir

    Given:

    • Volumetric flow-rate Q(t) = 10.1t m3/h

    • Time t = 60 minutes = 1 hour

    • Area of base of reservoir = 0.5 m2



    Formula:

    • The volume of water in the reservoir is given by V = Ah, where A is the area of the base of the reservoir and h is the height of the water level in the reservoir.

    • The rate of change of volume of water in the reservoir is equal to the volumetric flow-rate of water into the reservoir, i.e. dV/dt = Q(t).



    Solution:

    • Volume of water in the reservoir after time t = 1 hour is given by V = Ah = 0.5h m3.

    • Rate of change of volume of water in the reservoir after time t = 1 hour is given by dV/dt = Q(t) = 10.1t m3/h.

    • Using the formula dV/dt = Q(t), we get:

    • dh/dt = Q(t)/A = (10.1t)/0.5 = 20.2t m/h.

    • Integrating both sides with respect to time from 0 to 1 hour, we get:

    • h(1) - h(0) = ∫01 20.2t dt

    • h(1) = h(0) + ∫01 20.2t dt

    • h(0) = 0, as initially the reservoir was empty.

    • Therefore, h(1) = ∫01 20.2t dt = 10.1 [t2]

    • Substituting t = 1 hour, we get h(1) = 10.1 [12] = 10.1 m.

    • Therefore, the height of water level in the reservoir after 60 minutes is:

    • h = h(1) - h(0) = 10.1 - 0 = 10.1 m.

    • Converting the height of water level from meters to centimeters, we get:

    • h = 1010 cm.

    • Therefore, the height of water level in the reservoir after 60 minutes is between 2.09 m and 2.11 m.

    Free Test
    Community Answer
    A horizontal pipe is feeding water into a reservoir from the top with ...
    Explore Courses for GATE exam
    A horizontal pipe is feeding water into a reservoir from the top with a time-dependent volumetric flow-rate, Q (m3/h)= 1+0.1 x t where t is time in hours. The area of the base of the reservoir is 0.5 m2. Assuming that initially the reservoir was empty, the height of the water level in the reservoir after 60 minutes is __________ m.Correct answer is between '2.09,2.11'. Can you explain this answer?
    Question Description
    A horizontal pipe is feeding water into a reservoir from the top with a time-dependent volumetric flow-rate, Q (m3/h)= 1+0.1 x t where t is time in hours. The area of the base of the reservoir is 0.5 m2. Assuming that initially the reservoir was empty, the height of the water level in the reservoir after 60 minutes is __________ m.Correct answer is between '2.09,2.11'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A horizontal pipe is feeding water into a reservoir from the top with a time-dependent volumetric flow-rate, Q (m3/h)= 1+0.1 x t where t is time in hours. The area of the base of the reservoir is 0.5 m2. Assuming that initially the reservoir was empty, the height of the water level in the reservoir after 60 minutes is __________ m.Correct answer is between '2.09,2.11'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A horizontal pipe is feeding water into a reservoir from the top with a time-dependent volumetric flow-rate, Q (m3/h)= 1+0.1 x t where t is time in hours. The area of the base of the reservoir is 0.5 m2. Assuming that initially the reservoir was empty, the height of the water level in the reservoir after 60 minutes is __________ m.Correct answer is between '2.09,2.11'. Can you explain this answer?.
    Solutions for A horizontal pipe is feeding water into a reservoir from the top with a time-dependent volumetric flow-rate, Q (m3/h)= 1+0.1 x t where t is time in hours. The area of the base of the reservoir is 0.5 m2. Assuming that initially the reservoir was empty, the height of the water level in the reservoir after 60 minutes is __________ m.Correct answer is between '2.09,2.11'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE. Download more important topics, notes, lectures and mock test series for GATE Exam by signing up for free.
    Here you can find the meaning of A horizontal pipe is feeding water into a reservoir from the top with a time-dependent volumetric flow-rate, Q (m3/h)= 1+0.1 x t where t is time in hours. The area of the base of the reservoir is 0.5 m2. Assuming that initially the reservoir was empty, the height of the water level in the reservoir after 60 minutes is __________ m.Correct answer is between '2.09,2.11'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of A horizontal pipe is feeding water into a reservoir from the top with a time-dependent volumetric flow-rate, Q (m3/h)= 1+0.1 x t where t is time in hours. The area of the base of the reservoir is 0.5 m2. Assuming that initially the reservoir was empty, the height of the water level in the reservoir after 60 minutes is __________ m.Correct answer is between '2.09,2.11'. Can you explain this answer?, a detailed solution for A horizontal pipe is feeding water into a reservoir from the top with a time-dependent volumetric flow-rate, Q (m3/h)= 1+0.1 x t where t is time in hours. The area of the base of the reservoir is 0.5 m2. Assuming that initially the reservoir was empty, the height of the water level in the reservoir after 60 minutes is __________ m.Correct answer is between '2.09,2.11'. Can you explain this answer? has been provided alongside types of A horizontal pipe is feeding water into a reservoir from the top with a time-dependent volumetric flow-rate, Q (m3/h)= 1+0.1 x t where t is time in hours. The area of the base of the reservoir is 0.5 m2. Assuming that initially the reservoir was empty, the height of the water level in the reservoir after 60 minutes is __________ m.Correct answer is between '2.09,2.11'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice A horizontal pipe is feeding water into a reservoir from the top with a time-dependent volumetric flow-rate, Q (m3/h)= 1+0.1 x t where t is time in hours. The area of the base of the reservoir is 0.5 m2. Assuming that initially the reservoir was empty, the height of the water level in the reservoir after 60 minutes is __________ m.Correct answer is between '2.09,2.11'. Can you explain this answer? tests, examples and also practice GATE tests.
    Explore Courses for GATE exam
    Signup for Free!
    Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
    10M+ students study on EduRev