Please show work, Thanks! A horizontal pipe carries a smoothly flowing liquid wi

Question

Please show work, Thanks!

A horizontal pipe carries a smoothly flowing liquid with density 1.35 x 103 kg/m3. At locations 1 and 2 along the pipe the diameters are 6.57 cm and 2.15 cm, respectively. Is the flow speed at location 2 higher or lower than at location 1? 6.57 cm 2 2.15 cm O Higher O O Can't tell rom the data Can't tell from the data O Lower The flow speed at location 1 is 2.95 m/s. What is the flow speed at location 2? (Notice that the two locations are at the same elevation.) 2.75 at the same elevation.) 2.75 * 10 101 Number m/s

Explanation / Answer

given,

diameter of location 1 = 6.57 cm

diameter of location 2 = 2.15 cm

by continuity equation

area1 * velocity1 = area2 * velocity2

since the area of the area2 is less the velocity will be higher than location 1

speed at location1 = 2.95 m/s

(pi * (6.57 * 10^-2)^2 / 4) * 2.95 = (pi * (2.15 * 10^-2)^2 / 4) * x

x = 27.547 m/s

speed at location2 = 27.547 m/s

by bernoulli's equation

P1 + 0.5 * rho * v1^2 = P2 + 0.5 * rho * v2^2

P1 - P2 = 0.5 * rho * (v2^2 - v1^2)

pressure difference = 0.5 * 1.35 * 10^3 * (27.547^3 - 2.95^2)

presssure difference = 14104115.615 Pa

pressure at location 2 will be lower than at location1

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