A horizontal pipe carries a smoothly flowing liquid with density 1.11 × 103 kg/m

Question

A horizontal pipe carries a smoothly flowing liquid with density 1.11 × 103 kg/m3. At locations 1 and 2 along the pipe the diameters are 6.75 cm and 3.23 cm respectively. Is the flow speed at location 2 higher or lower than at location 1? O Lower O Can't tell from the data O Higher 6.75 cm 2: 13.23 cm 2 3.23 cm The flow speed at location 1 is 1.81 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 Higher O Lower O Can't tell O Can't tell

Explanation / Answer

according to equation of continuity

A1*v1 = A1*v2

v2/v1 = A1/A2

A1 = pi*r1^2

A2 = pi*r2^2

v2/v1 = r1^2/r2^2

r1 > r2

v2 > v1

speed at 2 is lower than 1

+++++++++++++++

v2 = r1^2*v1/r2^2 = (r1/r2)^2*v1 = (6.75/3.23)^2*1.81 = 7.904 m/s

from bernoullis theorem

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

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

P2 - P1 = 0.5*1.11*10^3*(1.81^2-7.904^2)

P2 - P1 = -32854.4 Pa

++++

lower

from equation of continuity

v2 = (d1/d2)^2*v1

v2 = (11.3/16.7)^2*9.49 = 4.34 m/s

from bernoullis thetrem

P1 + 0.5*rho*v1^2 + rho*g*h1 = P2 + 0.5*rho*v2^2

P2 - P1 = -0.5*rho*v2^2 + 0.5*rho*v1^2 + rho*g*h1

P1 - P2 = (0.5*1.35*10^3*9.49^2)+(1.35*10^3*9.8*8.61) -(0.5*1.35*10^3*4.34^2)

P1 - P2 = 1.61*10^5 Pa

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