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A two-dimensional duct contains a straight sided contraction as in Fig. 3.29. The depth is constant at 30 cm. At a certain time an incompressible fluid flows in the duct at a rate of 0.3 m3 /s and is decreasing at the rate of 0.1 m3 /s per second. Esti mate the acceleration at the section AA 20 cm from the inlet.?
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A two-dimensional duct contains a straight sided contraction as in Fig...
Given Information:


  • Two-dimensional duct containing a straight sided contraction

  • Depth is constant at 30 cm

  • Fluid flows in the duct at a rate of 0.3 m3 /s

  • Fluid flow is decreasing at the rate of 0.1 m3 /s per second

  • Section AA is 20 cm from the inlet



Solution:


  • Step 1: Find the area of the section AA


    • Area = Depth x Width

    • Width at the section AA = Width at the inlet = 2 x Depth = 2 x 30 cm = 60 cm = 0.6 m

    • Area at the section AA = Depth x Width = 0.3 x 0.6 = 0.18 m2


  • Step 2: Find the velocity of the fluid at the section AA


    • Volume flow rate = Area x Velocity

    • Velocity = Volume flow rate / Area

    • Initial volume flow rate = 0.3 m3 /s

    • Decrease in volume flow rate per second = 0.1 m3 /s

    • Volume flow rate at the section AA at the given time = Initial volume flow rate - (Decrease in volume flow rate per second x Time)

    • Time elapsed = 20 cm / Velocity at the section AA

    • Volume flow rate at the section AA = 0.3 - (0.1 x Time elapsed)

    • Volume flow rate at the section AA = 0.3 - (0.1 x (0.2 / Velocity at the section AA))

    • Velocity at the section AA = 1.5 m/s


  • Step 3: Find the acceleration at the section AA


    • Acceleration = (Change in Velocity) / Time

    • Change in Velocity = Velocity at the section AA - Velocity at the inlet

    • Velocity at the inlet = Volume flow rate / (Depth x Width at the inlet) = 0.3 / (0.3 x 0.6) = 1 m/s

    • Change in Velocity = 1.5 - 1 = 0.5 m/s

    • Time = Distance / Velocity at the section AA = 0.2 / 1.5 = 0.133 s

    • Acceleration = 0.5 / 0.133 = 3.76 m/s2


  • Step 4: Answer


    • Acceleration at the section AA, 20 cm from the inlet, is 3.76 m/s2


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A two-dimensional duct contains a straight sided contraction as in Fig. 3.29. The depth is constant at 30 cm. At a certain time an incompressible fluid flows in the duct at a rate of 0.3 m3 /s and is decreasing at the rate of 0.1 m3 /s per second. Esti mate the acceleration at the section AA 20 cm from the inlet.?
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A two-dimensional duct contains a straight sided contraction as in Fig. 3.29. The depth is constant at 30 cm. At a certain time an incompressible fluid flows in the duct at a rate of 0.3 m3 /s and is decreasing at the rate of 0.1 m3 /s per second. Esti mate the acceleration at the section AA 20 cm from the inlet.? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A two-dimensional duct contains a straight sided contraction as in Fig. 3.29. The depth is constant at 30 cm. At a certain time an incompressible fluid flows in the duct at a rate of 0.3 m3 /s and is decreasing at the rate of 0.1 m3 /s per second. Esti mate the acceleration at the section AA 20 cm from the inlet.? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A two-dimensional duct contains a straight sided contraction as in Fig. 3.29. The depth is constant at 30 cm. At a certain time an incompressible fluid flows in the duct at a rate of 0.3 m3 /s and is decreasing at the rate of 0.1 m3 /s per second. Esti mate the acceleration at the section AA 20 cm from the inlet.?.
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