Question

A 4.70 cm radius pipe has ethanol flowing through it at 6.00 m/s. The pipe then...

A 4.70 cm radius pipe has ethanol flowing through it at 6.00 m/s. The pipe then rises by 7.00 m and increases in radius to 11.3 cm. The pipe then empties into the air.
(a) What is the pressure within the ethanol in the first 4.70 cm radius segment?
____ Pa
(b) How fast is the ethanol in the second 11.3 cm radius segment?
___ m/s

Homework Answers

Answer #1


from equation of continuity


volume flow rate remains same in a fluid flow

A1*v1 = A2*v2

A1 = pi*r1^2


A2 = pi*r2^2


r1 = radius of smaller pipe = 4.7 cm = 0.047 m

r2 = radius of larger pipe = 11.3 cm = 0.113 m


v1 = 6 m/s

v2 = ?


r1^2*v1 = r2^2*v2


v2 = v1*(r1/r2)^2

v2 = 6*(0.047/0.113)^2


v2 = 1.04 m/s

==================


from Bernoullis principle

P1 + (1/2)*rho*v1^2 + rho*g*h1 = P2 + (1/2)*rho*v2^2 + rho*g*h2

P1 = P2 + (1/2)*rho*(v2^2 - v1^2) + rho*g*(h2 - h1)

h1 = 0


h2 = 7 m


rho = density of ethanol = 789 kg/m^3


P2 = 10^5 Pa


v1 = 6 m/s

v2 = 1.04 m/s


P1 = 10^5 + (1/2)*789*(1.04^2-6^2) + 789*9.8*7

P1 = 1.4*10^5 Pa <<<<<----------ANSWER

=======================

part(b)


v2 = 1.04 m/s

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