# Question As shown in the figure below, an incompressible liquid of density p flows steadily and horizontally in a circular cross-sectional pipe. At section (1), the velocity profile over the cross-sectional area is uniform at Uo. At section (2), the flow is turbulent, and the velocity profile is u = Umat (1 r/R)1/8, where Umer is the centerline velocity in the axial z-direction. R is the pipe radius, and r is the radius from the pipe axis. The pressure at sections (1) and (2) are P: = 51 kPa (guage) and P2 = 50 kPa (gauge). respectively. Ignore the effects of gravity. Assume p = 1000 kg/m?, R=1 cm and Up = 5 m/s. Determine the magnitude of the wall frictional force D acting on the liquid between sections (1) and (2) D=1N. Section (1) (P1 Section (2) D Z vo u(r)

G8LYXK The Asker · Mechanical Engineering

Transcribed Image Text: As shown in the figure below, an incompressible liquid of density p flows steadily and horizontally in a circular cross-sectional pipe. At section (1), the velocity profile over the cross-sectional area is uniform at Uo. At section (2), the flow is turbulent, and the velocity profile is u = Umat (1 r/R)1/8, where Umer is the centerline velocity in the axial z-direction. R is the pipe radius, and r is the radius from the pipe axis. The pressure at sections (1) and (2) are P: = 51 kPa (guage) and P2 = 50 kPa (gauge). respectively. Ignore the effects of gravity. Assume p = 1000 kg/m?, R=1 cm and Up = 5 m/s. Determine the magnitude of the wall frictional force D acting on the liquid between sections (1) and (2) D=1N. Section (1) (P1 Section (2) D Z vo u(r)
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Transcribed Image Text: As shown in the figure below, an incompressible liquid of density p flows steadily and horizontally in a circular cross-sectional pipe. At section (1), the velocity profile over the cross-sectional area is uniform at Uo. At section (2), the flow is turbulent, and the velocity profile is u = Umat (1 r/R)1/8, where Umer is the centerline velocity in the axial z-direction. R is the pipe radius, and r is the radius from the pipe axis. The pressure at sections (1) and (2) are P: = 51 kPa (guage) and P2 = 50 kPa (gauge). respectively. Ignore the effects of gravity. Assume p = 1000 kg/m?, R=1 cm and Up = 5 m/s. Determine the magnitude of the wall frictional force D acting on the liquid between sections (1) and (2) D=1N. Section (1) (P1 Section (2) D Z vo u(r)
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DSK2LN

Soln:{:[u=U_(max)(1-gamma//R)^(1//6)],[P_(1)=52kPa],[P_(2)=50kPa],[U_(0)=5m//s],[rho=1000kylm^(3)","R=1cm]:}From momentum equation.F=(P_(1)A_(1)-P_(2)A_(2)^('))+m( bar(V)_(1)- bar(V)_(2))" (1) "For mass conservation.{:[m_(1)^(')=m_(2)^(')],[rh ... See the full answer