(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The alaskan pipeline has a capacity of 2.37*10^{5}m^{3}/day of oil per day. Along most of the pipeline the radius is 60 cm. Find the pressure at a point where the pipe has a 35 cm radius. Take the pressure in the section with radius 60 cm to be 160 kPa and the density of oil to be 800kg/m^{3}. Answer in units of kPA

2. Relevant equations

.5 * rho * v_{1}^{2}+ rho * g * y + p_{1}= .5 * rho * v_{2}^{2}+ rho * g* y + p_{2}

since y = 0, we end up with:

.5 * rho * v_{1}^{2}+ p_{1}= .5 * rho * v_{2}^{2}+ p_{2}

v_{2}= v_{1}( A_{1}/ A_{2})

3. The attempt at a solution

v1 = 2.37x10^5 m^3/day = 2.743055556 m^3/sec

A1 = 60^2*pi = 11309.73355 cm^2

A2 = 35^2 * pi = 3848.451001 cm^2

v2 = v1 * (A1/A2)

p1-p2 (difference in pressure) = (.5)(rho)(v2^2) - (.5)(rho)(v1^2)

substitute:

= (.5)(rho) ((v1*A1/A2)^2) - (.5)(rho)(v1^2)

= (.5)(rho)(v1^2) [(a1/a2)^2 - 1]

plugging in:

= (0.5)(800)(2.743055556)^2 (7.636401493) = 22983.59459 Pa = p1-p2

since we're given p1 = 160 kPa, converting the difference in pressure to kPa and subtracting yields

22.98359459 = 160 - p2

p2 = 137.0164054 kPa

However, this is an in correct answer. Does anyone see where I'm making my mistake?

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# Homework Help: Difference in pressure question

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