8. Water flows through a pipe of variable cross-sectional area above level groun

Question

8. Water flows through a pipe of variable cross-sectional area above

level ground. The lower level of the pipe has a cross-sectional area of

0.06 m2, while the upper level has an area of 0.02 m2; the pipe ascends a

height of 2.0 m. The mass flow rate through the pipe is 40 kg/s.

(a)Determine the speed of the water through the lower level of the

pipe.

(b) Determine the speed of the water through the upper level of

the pipe.

(c) Determine the magnitude of the pressure difference between the

two levels.

(d) Which level is at the highest pressure?

Explanation / Answer

Area at the lower level = (Pi/4 )dlower2 = 0.002827 m2
Area at the upper level = (Pi/4 )dupper2 = 0.000314 m2
(a)
Now the mass flow rate is constant throughout the pipe because water is incompressible liquid.
theefore m = pALVL
VL = 14.149 m/s
(b) m = pAUVU
VU = m/pAU = 127.38 m/s
Where VL and VU is the velocity in lower and upper end.
(c) From bernoullis equation
(PL - PU) / pg = (VU2 - VL2) / 2g + (ZU - ZL)
where p is the density of water , L represent lower and U represent upper
Z is height and P is the pressure
ZU - ZL = 2 (given)
(PL - PU) = 80.33*105 N/m2
(d) lower level is at highest pressure.

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