Explanations & Calculations
- To workout this, it is necessary to assume water flows in laminar flow such that Bernoulli's equation could be applied.
- Since the pipe is horizontal, the regular Bernoulli equation reduces down to,
P1+21ρv12=P2+21ρv22
- Subjecting the final pressure: P2 gives,
P2=P1+21ρ(v12−v22)
- Then it is about finding the final speed:v2.
- The initial pressure is given in atm which needs to be converted into Pascal before substituting,. Then,
4.86atm=4.86×1.01325×105Pa=492439.5Pa
- Since the water was assumed incompressible, volumetric flow is consistent thoughout. Then,
Q=A1v1=A2v2
- Now A2=6.441A1→A2A1=6.44
- Rearranging for Q gives,
A2A1=v1v2=6.44
v2=6.44×2.27ms−1=14.6188ms−1
- Therefore, the final pressure is,
P2=492439.5Pa+21×1000kgm−3×(2.272−14.61882)=338461.3Pa=1.01325×105338461.3Pa=3.34atm
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