Question

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

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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