Cuisluer the og system pum Free pipe zs unknown P4 Reservoir

Cuisluer the og system pum Free pipe zs unknown ·P4 Reservoir (a) System A Free Ps pipe zs = 1.7m ·P4 Reservoir b) System B Figure 1: Systems A and B for homework problem 1 For both systems: Consider water at 20 degrees Celsius flowing through the following system. Neglect frictional losses h. The reservoir surface area is 2m2 and the cross-sectional area everywhere in the pipe is 0.05 m2. (a) For System A: Which is larger: Pl or P3? Justify your answer (b) For System B: Which is larger: P1 or P3? Justify your answer. (c) Explain why System B is less likely to cause the water to cavitate. (d) In System B, if you want the velocity at the free jet to be 2 m/s, how much head hp must the pump add?

Solution

a) P1 is larger because from Bernoulli\'s principle P1 + V₁²/2g +h₁= P3 +V₃²/2g+h₃

Or P1 +0= P3 +V3²/2g (as there is fluid velocity in pipe and not at reservoir surface, h₁=h₃)

Hence P1 > P3

b) P3 is larger because of the following:

Considering reservoir surface as datum P3+h₃+ V₃²/(2g) = P5 +h₅+V₅²/(2g)

P1=P5, h₃=0, V₃₌V₅ (from contuinuity)

Therefore P3= P1+h₅

Hence P3 > P1

c) Since the pump suction is flooded for system B i.e. there positive imposed pressure at pump suction, there is less chance the static pressure at pump suction will go below the water saturated vapour pressure at 20 deg C. But for system A the pump suction is at vacuum(negative gauge pressure) condition. Threrfore it is more likely that the pump suction pressure will be so low such that is reaches saturated vapour pressure at 20 deg C. Hence system A is more likely to cavitate.

d) The required pump head(TDH) is sum of velocity pressure and static head differences between suction and discharge.

H_pump=(1.7-1) + 2²/(2x9,81) (Note: pressure head difference is 0 as P1 =P5, friction neglected. Overall head is differences are considered across sections 1 and 5 which is equivalent to considering the same at actual pump suction and discharge.)

Or H_pump= 0.9 m