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Answer question 2 only
(1) A horizontal pipe expands smoothly from diameter do to a larger diameter d₁. A liquid of
density p flows at speed vo through the pipe. If the pressure in the narrower section is Po,
find an expression for the pressure pl in the wider section.
(2) A pressure gauge reads 50 kPa as water flows at 10.0 m/s through a 16.8 cm-diameter hori-
zontal pipe. What is the reading of a pressure gauge after the pipe has expanded to 20.0 cm
in diameter?
Transcribed Image Text:(1) A horizontal pipe expands smoothly from diameter do to a larger diameter d₁. A liquid of density p flows at speed vo through the pipe. If the pressure in the narrower section is Po, find an expression for the pressure pl in the wider section. (2) A pressure gauge reads 50 kPa as water flows at 10.0 m/s through a 16.8 cm-diameter hori- zontal pipe. What is the reading of a pressure gauge after the pipe has expanded to 20.0 cm in diameter?
Expert Solution
Step 1: Given Information

I n i t i a l space p r e s s u r e comma p subscript 1 equals 50 cross times 10 cubed P a
V e l o c i t y space o f space w a t e r comma v subscript 1 equals 10 space m divided by s
D i a m e t e r comma d subscript 1 equals 16.8 space c m equals 0.168 space m
D i a m e t e r comma d subscript 2 equals 20 space c m equals 0.20 space m

From the continuity equation

A subscript 1 v subscript 1 equals A subscript 2 v subscript 2
v subscript 2 equals fraction numerator A subscript 1 v subscript 1 over denominator A subscript 2 end fraction
space space space space equals v subscript 1 open parentheses d subscript 1 over d subscript 2 close parentheses squared
space space space space equals 10 cross times open parentheses fraction numerator 0.168 over denominator 0.20 end fraction close parentheses squared
space space space space equals 7.056 space m divided by s


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