23. Pumps 1: Power and Pump Curves CH EN 374: Fluid Mechanics

How do pumps add energy? IN OUT Assume 𝐷 1 = 𝐷 2 Assume 𝑧 1 ≈ 𝑧 2 Assume no friction 𝑃 2 − 𝑃 1 𝜌 + 1 2 𝛼 𝑣 2 2 − 𝑣 1 2 +𝑔( 𝑧 2 − 𝑧 1 )= 𝑤 𝑠 − 𝑤 𝑓 𝑤 𝑠 = 𝑃 2 − 𝑃 1 𝜌 = Δ P pump 𝜌 Is Δ 𝑃 𝑝𝑢𝑚𝑝 positive or negative? Pump puts energy into the fluid in form of pressure.

Pump Head Expresses energy addition in the form of a head (length) How do we get heads from Δ𝑃′𝑠? ℎ 𝑝 = Δ 𝑃 pump 𝜌𝑔

Pumping Power 𝑤 𝑠 = Δ P pump 𝜌 = 𝑚 𝜌 Δ 𝑃 𝑝𝑢𝑚𝑝 𝑊 𝑠 = 𝑚 𝑤 𝑠 = 𝑉 Δ 𝑃 𝑝𝑢𝑚𝑝 Dimensions: energy/mass We want power (dimensions: energy/time) = 𝑚 𝜌 Δ 𝑃 𝑝𝑢𝑚𝑝 𝑊 𝑠 = 𝑚 𝑤 𝑠 = 𝑉 Δ 𝑃 𝑝𝑢𝑚𝑝

Pumping Power 𝑊 𝑝𝑢𝑚𝑝 = 𝑉 Δ P pump

Problem Water Tank Shower Pump 1 2 3 A pump moves water from a tank at ground level to a shower on the third floor. Find Δ 𝑃 𝑝𝑢𝑚𝑝 from the mechanical energy balance between 1 and 3. (Include head loss)

Δ 𝑃 𝑝𝑢𝑚𝑝 =𝜌𝑔Δ𝑧+Δ 𝑃 𝑙𝑜𝑠𝑠 h p =Δ𝑧+ h L

ℎ 𝑝 = ℎ 𝑝 Operating Point From System From Pump Depends on 𝑽 𝒉 𝐩 =𝚫𝒛+ 𝐡 𝐋 Relationship is different for each pump 𝒉 𝑳 depends on 𝑽 Operating point: where ℎ 𝑝 and 𝑉 is same from both sides

Pump Curve 𝒉 𝒑 𝑽 Supply Curve System Curve Experimentally Determined Calculated from MechE Balance

𝜂= 𝑊 𝑝𝑢𝑚𝑝 𝑊 𝑒𝑙𝑒𝑐 Pump Efficiency Energy to Fluid 𝜂= 𝑊 𝑝𝑢𝑚𝑝 𝑊 𝑒𝑙𝑒𝑐 Electricity required by pump

Efficiency Curve 𝒉 𝒑 𝑽 𝜼

𝒉 𝒑 𝑽 Supply Curve https://www.youtube.com/watch?v=qtikLU0EC2Q How would you find the maximum head supplied by the pump? Maximum flowrate?

𝒉 𝒑 𝑽 Supply Curve Maximum head: shutoff head Maximum flowrate: free delivery Demo: https://www.youtube.com/watch?v=qtikLU0EC2Q

Problem An operation requires 370 gpm of water and a net head of about 24 ft. You have decided to order a TACO Model 4013 pump for this application. Which should you order, the 8.25-in impeller model or the 12.75-in?