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A horizontal pipe carries a smoothly flowing liquid with density 1.39 × 103 kg/m3. At locations...

A horizontal pipe carries a smoothly flowing liquid with density 1.39 × 103 kg/m3. At locations 1 and 2 along the pipe the diameters are 5.23 cm and 2.19 cm, respectively. The flow speed at location 1 is 1.79 m/s. What is the pressure difference between location 2 and location 1 (including its sign)? Ignore viscosity.

Expert Solution

Gravitational acceleration = g = 9.81 m/s²

Density of the fluid = = 1390 kg/m³

Diameter of pipe at location 1 = D₁ = 5.23 cm = 0.0523 m

Diameter of pipe at location 2 = D₂ = 2.19 cm = 0.0219 m

Area of pipe at location 1 = A₁

A₁ = D₁²/4

Area of pipe at location 2 = A₂

A₂ = D₂²/4

Flow speed of fluid at location 1 = V₁ = 1.79 m/s

Flow speed of fluid at location 2 = V₂

By continuity equation,

A₁V₁ = A₂V₂

(D₁²/4)V₁ = (D₂²/4)V₂

D₁²V₁ = D₂²V₂

(0.0523)²(1.79) = (0.0219)²V₂

V₂ = 10.208 m/s

Pressure of fluid at location 1 = P₁

Pressure of fluid at location 2 = P₂

The pipe is horizontal, therefore the height of the pipe at location 1 and 2 is same.

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

By Bernoulli's Equation,

P = -70194.42 Pa

Pressure difference between location 2 and location 1 = -70194.42 Pa

genius_generous answered 1 hour ago

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