Aerospace Engineering > GATE 2014 > Pipe Flow
Two overflowing water reservoirs are connected with a100m long pipe of circular cross-section (of radius, R=0.02m), such that height difference h remains constant as shown in the figure below. The centerline velocity in the pipe is 10m/s. The velocity profile inside the pipe over the entire length is
u=-(R2/(4μ))dp/dx[1-r2/R2],
where, dp/dx is a constant pressure gradient along the pipe length, x is measured from theleft end of the pipe along its central axis and r is radial location inside the pipe with respect to its axis.(Given data: Density and kinematic viscosity of water are 1000kg/ms and 1×10-6m2/s respectively; acceleration due to gravity is 10m/s2). If all other losses except the frictional losses at the pipe wall are neglected, the value of h in meter is
u=-(R2/(4μ))dp/dx[1-r2/R2],
where, dp/dx is a constant pressure gradient along the pipe length, x is measured from theleft end of the pipe along its central axis and r is radial location inside the pipe with respect to its axis.(Given data: Density and kinematic viscosity of water are 1000kg/ms and 1×10-6m2/s respectively; acceleration due to gravity is 10m/s2). If all other losses except the frictional losses at the pipe wall are neglected, the value of h in meter is
Correct : 0.99 to 1.01
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