Answer to Question #106779 in Physical Chemistry for Bharti

Question

A 2m long pipelines tapers uniformly form 10cm diameter to 20cm diameters at its upper end. The pipe centreline slopes upwards at a angle of 30° to the horizontal and the flow direction is from smaller to bigger cross section. If the pressure gauges installed at lower and upper ends of the pipeline read 200kpa and 230kpa respectively. Determine the flow rate and the pressure mid length of the pipeline. Assume no energy losses.

Answer 1

A1*V1=A2*V2

A1=3.14/4*0.1² = 0.0314 m² cross section area 1

A2=3.14/4*0.2² = 0.00785 m² cross section area 2

0.0314V1 = 0.00785V2

Bernoulli's Equation:

200+1/2*1000*V1 = 230+1000*9.8*2cos30+1/2*1000V2

or simply V1² + V2² = 34

Solving the system of equations:

V1=6 , V2 = 2,6 - velocities

Average: = 4.1

Presure: (230+200)/2 = 215 kPa