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

2. 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 𝛼 𝑣 2 2 − 𝑣 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.

3. 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

4. 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

5. Pumping Power
𝑊 𝑝𝑢𝑚𝑝 = 𝑉 Δ P pump

6. 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)

7. Δ 𝑃 𝑝𝑢𝑚𝑝 =𝜌𝑔Δ𝑧+Δ 𝑃 𝑙𝑜𝑠𝑠
h p =Δ𝑧+ h L

8. 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

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

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

11. Efficiency Curve
𝒉 𝒑 𝑽 𝜼

14. 𝒉 𝒑 𝑽
Supply Curve
How would you find the maximum head supplied by the pump?
Maximum flowrate?

15. 𝒉 𝒑 𝑽 Supply Curve Maximum head: shutoff head
Maximum flowrate: free delivery
Demo:

16. 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 in?