Problem 3. Performance data for a pump are given in the table below. From a curve fit to the data, the pump curve is given by H, = H, – C, Q² whereHo = 180 ft and C, = 1.524 × 10-6 ft/gpm?. This pump is used to move water at STP between two open reservoirs with an elevation increase of Az = 50 ft through a commercial steel pipe of length L = 1200 ft and diameter D = 1.0 ft that contains two 90° elbows (equivalent length of 30 diameters) and an open gate valve (equivalent length of 8 diameters). The flow entrance and exit for the reservoirs are abrupt. (a) Plot the pump curve and system curve on the same figure. (b) Calculate the flowrate with the gate valve open. (c) Calculate the equivalent length for the gate valve in order to reduce the flowrate by half. NOTE: Your calculations for this problem will require iteration because the friction factor for this case does depend on Q. Thus, it is recommended you use either EES (see solution for Example 19 from lecture) or Excel to get converged values. Q (gpm) Н, (ft) 500 1000 1500 2000 2500 3000 179 176 165 145 119 84 43

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**Problem 3.** Performance data for a pump are given in the table below. From a curve fit to the data, the pump curve is given by \( H_p = H_0 - C_p \, Q^2 \) where \( H_0 = 180 \, \text{ft} \) and \( C_p = 1.524 \times 10^{-5} \, \text{ft/gpm}^2 \). This pump is used to move water at STP between two open reservoirs with an elevation increase of \( \Delta z = 50 \, \text{ft} \) through a commercial steel pipe of length \( L = 1200 \, \text{ft} \) and diameter \( D = 1.0 \, \text{ft} \) that contains two 90° elbows (equivalent length of 30 diameters) and an open gate valve (equivalent length of 8 diameters). The flow entrance and exit for the reservoirs are abrupt. 

**Tasks:**
(a) Plot the pump curve and system curve on the same figure.

(b) Calculate the flow rate with the gate valve open.

(c) Calculate the equivalent length for the gate valve in order to reduce the flow rate by half. 

**NOTE:** Your calculations for this problem will require iteration because the friction factor for this case does depend on \( Q \). Thus, it is recommended you use either EES (see solution for Example 19 from lecture) or Excel to get converged values.

| \( Q \) (gpm) | 0   | 500 | 1000 | 1500 | 2000 | 2500 | 3000 |
|--------------|-----|-----|------|------|------|------|------|
| \( H_p \) (ft) | 179 | 176 | 165  | 145  | 119  | 84   | 43   |
Transcribed Image Text:**Problem 3.** Performance data for a pump are given in the table below. From a curve fit to the data, the pump curve is given by \( H_p = H_0 - C_p \, Q^2 \) where \( H_0 = 180 \, \text{ft} \) and \( C_p = 1.524 \times 10^{-5} \, \text{ft/gpm}^2 \). This pump is used to move water at STP between two open reservoirs with an elevation increase of \( \Delta z = 50 \, \text{ft} \) through a commercial steel pipe of length \( L = 1200 \, \text{ft} \) and diameter \( D = 1.0 \, \text{ft} \) that contains two 90° elbows (equivalent length of 30 diameters) and an open gate valve (equivalent length of 8 diameters). The flow entrance and exit for the reservoirs are abrupt. **Tasks:** (a) Plot the pump curve and system curve on the same figure. (b) Calculate the flow rate with the gate valve open. (c) Calculate the equivalent length for the gate valve in order to reduce the flow rate by half. **NOTE:** Your calculations for this problem will require iteration because the friction factor for this case does depend on \( Q \). Thus, it is recommended you use either EES (see solution for Example 19 from lecture) or Excel to get converged values. | \( Q \) (gpm) | 0 | 500 | 1000 | 1500 | 2000 | 2500 | 3000 | |--------------|-----|-----|------|------|------|------|------| | \( H_p \) (ft) | 179 | 176 | 165 | 145 | 119 | 84 | 43 |
### Problem 6

Consider again the pump and piping system of Problem 3 with the gate valve open.

(a) Calculate the flowrate with two pumps in parallel.  
(b) Calculate the flowrate with two pumps in series.  
(c) Add to your plot from Problem 3 curves for two pumps in parallel and two pumps in series.  
(d) Briefly discuss if it would be better to operate with pumps in parallel or series and how your answer would change as the steepness of the system curve changes.
Transcribed Image Text:### Problem 6 Consider again the pump and piping system of Problem 3 with the gate valve open. (a) Calculate the flowrate with two pumps in parallel. (b) Calculate the flowrate with two pumps in series. (c) Add to your plot from Problem 3 curves for two pumps in parallel and two pumps in series. (d) Briefly discuss if it would be better to operate with pumps in parallel or series and how your answer would change as the steepness of the system curve changes.
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