Map Sapling Learning A horizontal pipe carries a smoothly flowing liquid with de

Question

Map Sapling Learning A horizontal pipe carries a smoothly flowing liquid with density 1.15 103 kg/m2. At locations 1 and 2 along the pipe the diameters are 6.71 cm and 3.31 respectively. Is the flow speed at location 2 higher or lower than at lcation 1 O Lower O Can't tell fom the data 6.71 cm 2 13.31 cm Higher The flow speed at location 1 is 1.17 m/s. What is the pressure difference between location 2 and location 1 (including its sign)? Ignore viscosity Number Pa Is the pressure at location 2 higher or lower than at location 1? O Can't tell O Higher

Explanation / Answer

Q1. As diameter at location 2 is smaller than location 1, hence the area at location 2 is smaller than location 1. As the volume of flowing fluid remains constant, so speed at location 2 is higher than location 1.

Q2. Applying the continuity equation

A1v1 = A2v2

where A1 = area of the pipe at location 1

  v1 = velocity at location 1

A2 = area of the pipe at location 2

  v2 = velocity at location 2

so, v2 = A1v1/A2 = (d1/d2)2 x v1 = (6.71/3.31)2 x 1.17 = 4.8 m/s

as the pipe is horizontal

the pressure difference between location 1 and 2= 1/2 x density x (v22 - v12 ) = 1/2 x 1150 x (4.82 - 1.172 ) = 12505.17 Pa

the pressure difference between location 2 and 1 = -12505.17 Pa

Q3.Pressure at location 2 is lower than location 1

all the best in the course work

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