Question

A horizontal pipe carries a smoothly flowing liquid of density of 1330 kg/m3. At Locations 1...

A horizontal pipe carries a smoothly flowing liquid of density of 1330 kg/m3. At Locations 1 and 2 along the pipe, the diameters are ?1=5.71 cm and ?2=2.33 cm, respectively. The flow speed at Location 1 is 2.07 m/s . What is the pressure difference Δ? between Location 2 and Location 1 (including its sign)? Ignore viscosity.

Homework Answers

Answer #1

Density of fluid = = 1330 kg/m3

Pressure at location 1 = P1

Pressure at location 2 = P2

Diameter of pipe at location 1 = d1 = 5.71 cm = 0.0571 m

Diameter of pipe at location 2 = d2 = 2.33 cm = 0.0233 m

Speed of flow at location 1 = V1 = 2.07 m/s

Speed of flow at location 2 = V2

Pressure difference between location 2 and 1 = P = P2 - P1

Area of pipe at location 1 = A1 = d12/4

Area of pipe at location 2 = A2 = d22/4

By continuity equation,

A1V1 = A2V2

(d12/4)V1 = (d22/4)V2

V1d12 = V2d22

(2.07)(0.0571)2 = V2(0.0233)2

V2 = 12.43 m/s

The pipe is horizontal, hence there is no height difference between locations 1 and 2.

By bernoulli's equation,

P1 + V12/2 = P2 + V22/2

P2 - P1 = (V12 - V22)/2

P = (1330)[(2.07)2 - (12.43)2]/2

P = - 99896.3 Pa

Pressure difference between location 2 and location 1 = - 99896.3 Pa

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