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Water flows through a smooth circular pipe under turbulent conditions. In the viscous sub-layer, the
velocity varies linearly with the distance from the wall. The Fanning friction factor is defined as,where tw is the shear stress at the wall of the pipe, ρ is the density of the fluid and is the average velocity of 1ms-1  through the pipe. For this flow condition, the friction factor f is 0.005. At a distance of 0.05 mm from the wall of the pipe (in the viscous sub-layer), the velocity (in  ms-1 ,rounded off to the third decimal place), is __________.
    Correct answer is '2.828'. Can you explain this answer?
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    Water flows through a smooth circular pipe under turbulent conditions....
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    Water flows through a smooth circular pipe under turbulent conditions....
    Tw=(ρu²/2)*f ;

    Tw= 1/2x 1000 x (1)² × 0.005 = 2.5

    From Newton's law of viscosity,
    μ = - T/(du/dr) ...(I)

    If y is the vertical distance from the wall, then
    rw=r+y --> r=rw-y.

    Since ( -dr )= (dy);
    T/r =Tw/rw;
    r~rw (for viscous sub-layer), Equation (I) becomes

    μ=T/(du/dy)
    (or)
    (du/dy)=(T/μ) =(Tw*r/rw*μ)=(Tw/μ) ..(II)

    Integrating equation (II) provides
    u= (Tw/μ)*y
    (or)
    u =(2.5*0.05*10^-3)/(1*10^-3)=0.125

    u =0.125 m/s
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    Water flows through a smooth circular pipe under turbulent conditions. In the viscous sub-layer, thevelocity varies linearly with the distance from the wall. The Fanning friction factor is defined as,where tw is the shear stress at the wall of the pipe, ρ is the density of the fluid and is the average velocity of 1ms-1through the pipe. For this flow condition, the friction factor f is 0.005. At a distance of 0.05 mm from the wall of the pipe (in the viscous sub-layer), the velocity (in ms-1 ,rounded off to the third decimal place), is __________.Correct answer is '2.828'. Can you explain this answer?
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    Water flows through a smooth circular pipe under turbulent conditions. In the viscous sub-layer, thevelocity varies linearly with the distance from the wall. The Fanning friction factor is defined as,where tw is the shear stress at the wall of the pipe, ρ is the density of the fluid and is the average velocity of 1ms-1through the pipe. For this flow condition, the friction factor f is 0.005. At a distance of 0.05 mm from the wall of the pipe (in the viscous sub-layer), the velocity (in ms-1 ,rounded off to the third decimal place), is __________.Correct answer is '2.828'. 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 Water flows through a smooth circular pipe under turbulent conditions. In the viscous sub-layer, thevelocity varies linearly with the distance from the wall. The Fanning friction factor is defined as,where tw is the shear stress at the wall of the pipe, ρ is the density of the fluid and is the average velocity of 1ms-1through the pipe. For this flow condition, the friction factor f is 0.005. At a distance of 0.05 mm from the wall of the pipe (in the viscous sub-layer), the velocity (in ms-1 ,rounded off to the third decimal place), is __________.Correct answer is '2.828'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Water flows through a smooth circular pipe under turbulent conditions. In the viscous sub-layer, thevelocity varies linearly with the distance from the wall. The Fanning friction factor is defined as,where tw is the shear stress at the wall of the pipe, ρ is the density of the fluid and is the average velocity of 1ms-1through the pipe. For this flow condition, the friction factor f is 0.005. At a distance of 0.05 mm from the wall of the pipe (in the viscous sub-layer), the velocity (in ms-1 ,rounded off to the third decimal place), is __________.Correct answer is '2.828'. Can you explain this answer?.
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