(1) All the holes have samediameter of your choice, i.e., d n = d for n = 1 to10

Question

(1) All the holes have samediameter of your choice, i.e., dn = dfor n = 1 to10, please make a plot of water jet heightH and jet volume flow rate Q as a function ofhole#, i.e., H=H(n) andQ=Q(n).

(2) As you can see, the volume flow rate is not same for the 10holes because of head loss. So let us try to make the hole sizevary in a linear fashion, i.e., dn = d+ (n-1)d for n = 1 to10. Then make aplot of H=H(n) andQ=Q(n) again for various d. Canyou find a d-value that will make the jet volume flow ratethe same for all holes?

(3) If the volume flow rate isstill not the same, can you design the hole sizes so that thefountain jet flow rate will be the same? The holes shall be largeenough to make a great fountain show.

Explanation / Answer

You can take the energy equation from the pump to the top of the water fountain in the first hole. On top of the fountain for each hole the velocity V2=0 and p2=0. The velocity and pressure for state 1 are given at the pump. The height at the pump can be taken as z1=0. Applying the energy equation and major and minor losses (the major loss due to the bigger diameter pipe and the minor loss due to entering the hole) you can acquire z2. However, I am unsure of how to apply the smaller diameter 'd' into the height equation, but if you assume major losses due to 'd' are negligible you can circumvent the problem. That is all I can help you in so far. I think we're in the same class together. I'll be working on the problem tonight and tomorrow morning. If you have made more progress than me, can you give me a few hints? Thanks. If I solve anything by tomorrow, I'll provide some feedback.

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