Find: minimum # of stages gal min Elev2=825 [ft] Q=500 n=1,780 [rpm] s=0 [ft] ns>1,500 3 4 5 6 Elev1= Find the minimum number of stages for the pump. [pause] In this problem, --- 415 [ft] #stages?

Find: minimum # of stages gal min Elev2=825 [ft] Q=500 n=1,780 [rpm] s=0 [ft] ns>1,500 3 4 5 6 Elev1= Groundwater is pump from an aquifer into an elevated storage tank. 415 [ft] #stages?

Find: minimum # of stages gal min Elev2=825 [ft] Q=500 n=1,780 [rpm] s=0 [ft] ns>1,500 3 4 5 6 Elev1= The elevation of the groundwater table, and the elevation of the water surface elevation in the tank are provided. There is no drawdown --- 415 [ft] #stages?

Find: minimum # of stages gal min Elev2=825 [ft] Q=500 n=1,780 [rpm] s=0 [ft] ns>1,500 3 4 5 6 Elev1= in the groundwater table resulting from the pumping. 415 [ft] #stages?

Find: minimum # of stages gal min Elev2=825 [ft] Q=500 n=1,780 [rpm] s=0 [ft] ns>1,500 3 4 5 6 Elev1= The flowrate, actual motor speed, and minimum specific speed are also provided. [pause] 415 [ft] #stages?

Find: minimum # of stages gal min Elev2=825 [ft] Q=500 n=1,780 [rpm] s=0 [ft] ns>1,500 n * Q ns= Δh3/4 Elev1= In English units, --- 415 [ft] #stages?

Find: minimum # of stages gal min Elev2=825 [ft] Q=500 n=1,780 [rpm] s=0 [ft] ns>1,500 n * Q ns= Δh3/4 Elev1= the specific speed, n sub s, of a pump, equals ---- 415 [ft] specific #stages? speed

Find: minimum # of stages gal min Elev2=825 [ft] Q=500 n=1,780 [rpm] s=0 [ft] ns>1,500 motor speed [rpm] n * Q ns= Δh3/4 Elev1= the actual motor speed, n, in revolutions per minute, times --- 415 [ft] specific #stages? speed

Find: minimum # of stages gal min Elev2=825 [ft] Q=500 n=1,780 [rpm] s=0 [ft] ns>1,500 motor speed [rpm] n * Q gal flowrate ns= min Δh3/4 Elev1= the square root of the flowrate, in gallons per minute, divided by --- 415 [ft] specific #stages? speed

Find: minimum # of stages gal min Elev2=825 [ft] Q=500 n=1,780 [rpm] s=0 [ft] ns>1,500 motor speed [rpm] n * Q gal flowrate ns= min Δh3/4 Elev1= the head added by the pump, in feet, raised to the 3/4s power. 415 [ft] added specific head [ft] #stages? speed

Find: minimum # of stages gal min Elev2=825 [ft] Q=500 n=1,780 [rpm] s=0 [ft] ns>1,500 motor speed [rpm] n * Q gal flowrate ns= min Δh3/4 Elev1= Since the problem statement provides the --- 415 [ft] added specific head [ft] #stages? speed

Find: minimum # of stages gal Elev2=825 [ft] Q=500 min n=1,780 [rpm] s=0 [ft] ns>1,500 motor speed [rpm] n * Q gal flowrate ns= min Δh3/4 Elev1= flowrate, motor speed, and minimum specific speed, we’ll solve for the added head --- 415 [ft] added specific head [ft] #stages? speed

Find: minimum # of stages gal Elev2=825 [ft] Q=500 min n=1,780 [rpm] s=0 [ft] ns>1,500 motor speed [rpm] n * Q gal flowrate ns= min Δh3/4 Elev1= and identify the minimum number of stages required. [pause] Solving for the added head, the added head equals --- 415 [ft] added specific head [ft] #stages? speed

Find: minimum # of stages gal Elev2=825 [ft] Q=500 min n=1,780 [rpm] s=0 [ft] ns>1,500 n * Q ns= Δh3/4 Elev1= the actual speed to the 4/3s power, times the flowrate, to the 2/3s power, divided by the specific speed, to the 4/3s power. [pause] 415 [ft] n4/3 * Q2/3 Δh= ns4/3 #stages?

Find: minimum # of stages gal Elev2=825 [ft] Q=500 min n=1,780 [rpm] s=0 [ft] ns>1,500 h Elev1= If we look at a pump curve we recall that ---- 415 [ft] #stages? Q

Find: minimum # of stages gal Elev2=825 [ft] Q=500 min n=1,780 [rpm] s=0 [ft] A B ns>1,500 h pump A pump B Elev1= the total flowrate, resulting from multiple pumps operating in parallel, --- 415 [ft] #stages? Q

Find: minimum # of stages gal Elev2=825 [ft] Q=500 min n=1,780 [rpm] s=0 [ft] A B ns>1,500 h pump A pump B Elev1= is the sum of the flowrates, from each individual pump, for a given head. Similarly, 415 [ft] system Qsys=QA+QB #stages? Q

Find: minimum # of stages gal Elev2=825 [ft] Q=500 min n=1,780 [rpm] s=0 [ft] ns>1,500 h D C Elev1= the total head, resulting from multiple pumps operating in series, --- 415 [ft] pump C #stages? pump D Q

Find: minimum # of stages gal Elev2=825 [ft] Q=500 min n=1,780 [rpm] s=0 [ft] ns>1,500 h D C system Elev1= is the sum of heads, from each individual pump, for a given flowrate. When a single pump is fitted with multiple stages---- hsys=hC+hD 415 [ft] pump C #stages? pump D Q

Find: minimum # of stages gal Elev2=825 [ft] Q=500 min n=1,780 [rpm] s=0 [ft] ns>1,500 h D C system Elev1= each set of impellers, or bowls, can be thought of as separate pumps operating in series. Therefore, --- hsys=hC+hD 415 [ft] pump C #stages? pump D Q

Find: minimum # of stages gal Elev2=825 [ft] Q=500 min n=1,780 [rpm] s=0 [ft] ns>1,500 h D C system Elev1= if the change in head, or lift, generated by the pump is a fixed quantity, then the required lift for ---- hsys=hC+hD 415 [ft] pump C #stages? pump D Q

Find: minimum # of stages gal Elev2=825 [ft] Q=500 min n=1,780 [rpm] s=0 [ft] ns>1,500 h D C system Elev1= each stage, is inversely proportional to --- hsys=hC+hD 415 [ft] pump C #stages? pump D Q

Find: minimum # of stages gal Elev2=825 [ft] Q=500 min n=1,780 [rpm] s=0 [ft] ns>1,500 h 4 stages 3 stages 2 stages Elev1= the number of stages in the well casing. [pause] Therefore, if the value of delta h is known, --- 415 [ft] 1 stage #stages? Q

Find: minimum # of stages gal Elev2=825 [ft] Q=500 min n=1,780 [rpm] s=0 [ft] ns>1,500 h Δh Elev1= and the pump has 4 stages, as shown here, then for a given flowrate, Q, --- 415 [ft] #stages? Q

Find: minimum # of stages gal Elev2=825 [ft] Q=500 min n=1,780 [rpm] s=0 [ft] ns>1,500 h Δh Elev1= the total head produced by the pump is shared equally ---- 415 [ft] #stages? Q Q

Find: minimum # of stages gal Elev2=825 [ft] Q=500 min n=1,780 [rpm] s=0 [ft] ns>1,500 h Δh Elev1= Δh4 between the four stages. [pause] If there were only 3 stages, 415 [ft] Δh3 Δh2 #stages? Δh1 Q Q

Find: minimum # of stages gal Elev2=825 [ft] Q=500 min n=1,780 [rpm] s=0 [ft] ns>1,500 h Δh Elev1= each individual stage would be required to add more head to the system. [pause] Same is true for if there were only --- Δh3 415 [ft] Δh2 #stages? Δh1 Q Q

Find: minimum # of stages gal Elev2=825 [ft] Q=500 min n=1,780 [rpm] s=0 [ft] ns>1,500 h Δh Elev1= 2 stages, or 1 stage. 415 [ft] Δh2 #stages? Δh1 Q Q

Find: minimum # of stages gal Elev2=825 [ft] Q=500 min n=1,780 [rpm] s=0 [ft] ns>1,500 h Δh Elev1= [pause] From before, the equation for the specific speed --- 415 [ft] Δh1 #stages? Q Q

Find: minimum # of stages gal Elev2=825 [ft] Q=500 min n=1,780 [rpm] s=0 [ft] ns>1,500 n4/3 * Q2/3 = Δh h ns4/3 Δh Elev1= of the pump, n sub s, assumes there is only 1 stage. However, for a pump with multiple stages, ---- 415 [ft] Δh1 #stages? Q Q

Find: minimum # of stages gal Elev2=825 [ft] Q=500 min n=1,780 [rpm] s=0 [ft] ns>1,500 n4/3 * Q2/3 = Δh h ns4/3 Δh Elev1= the specific speed, is based on the head lift per stage, --- Δh3 415 [ft] Δh2 #stages? Δh1 Q Q

Find: minimum # of stages gal Elev2=825 [ft] Q=500 min n=1,780 [rpm] s=0 [ft] ns>1,500 Δh n4/3 * Q2/3 = h # stages ns4/3 Δh Elev1= and increases as the number of stages increases. [pause] The question asks to find the minimum ---- Δh3 415 [ft] Δh2 #stages? Δh1 Q Q

Find: minimum # of stages gal Elev2=825 [ft] Q=500 min n=1,780 [rpm] s=0 [ft] ns>1,500 Δh n4/3 * Q2/3 = h # stages ns4/3 Δh Elev1= number of stages, such that the the specific speed is at least --- Δh3 415 [ft] Δh2 #stages? Δh1 Q Q

Find: minimum # of stages gal Elev2=825 [ft] Q=500 min n=1,780 [rpm] s=0 [ft] ns>1,500 Δh n4/3 * Q2/3 = h # stages ns4/3 Δh Elev1= 1,500. [pause] Δh3 415 [ft] Δh2 #stages? Δh1 Q Q

Find: minimum # of stages gal Elev2=825 [ft] Q=500 min n=1,780 [rpm] s=0 [ft] ns>1,500 Δh n4/3 * Q2/3 = h # stages ns4/3 Δh Elev1= The minimum number of stages is a function of the ---- Δh3 415 [ft] Δh2 #stages? Δh1 Q Q

Find: minimum # of stages gal Elev2=825 [ft] Q=500 min n=1,780 [rpm] s=0 [ft] ns>1,500 Δh n4/3 * Q2/3 = h # stages ns4/3 Δh * ns4/3 = Δh # stages Elev1= the total head, the minimum specific speed, the motor speed, and the flowrate. [pause] n4/3 * Q2/3 415 [ft] #stages? Q Q

? Find: minimum # of stages = = n4/3 * Q2/3 ns4/3 n4/3 * Q2/3 gal Elev2=825 [ft] Q=500 min n=1,780 [rpm] s=0 [ft] ns>1,500 Δh n4/3 * Q2/3 = h # stages ns4/3 ? Δh * ns4/3 = Δh # stages Elev1= The last unknown variable is the change in head, delta h, which equals --- n4/3 * Q2/3 415 [ft] #stages? Q Q

? Find: minimum # of stages + + - + + ρ*g ρ*g = = n4/3 * Q2/3 ns4/3 gal Elev2=825 [ft] Q=500 min n=1,780 [rpm] s=0 [ft] ns>1,500 Δh n4/3 * Q2/3 = # stages ns4/3 ? Δh * ns4/3 = # stages Elev1= the total head of the water in the tank minus the total head of the ground. [pause] Assuming the pressure head and velocity head are negligible --- n4/3 * Q2/3 415 [ft] Ptank Pgw v2 v2 tank gw Δh = + ytank + - + ygw + ρ*g ρ*g 2*g 2*g

? Find: minimum # of stages + + - + + ρ*g ρ*g = = n4/3 * Q2/3 ns4/3 gal Elev2=825 [ft] Q=500 min n=1,780 [rpm] s=0 [ft] ns>1,500 Δh n4/3 * Q2/3 = # stages ns4/3 ? Δh * ns4/3 = # stages Elev1= in the tank and in the ground, the total head equation reduces to --- n4/3 * Q2/3 415 [ft] Ptank Pgw v2 v2 tank gw Δh = + ytank + - + ygw + ρ*g ρ*g 2*g 2*g

? Find: minimum # of stages = = n4/3 * Q2/3 ns4/3 n4/3 * Q2/3 gal Elev2=825 [ft] Q=500 min n=1,780 [rpm] s=0 [ft] ns>1,500 Δh n4/3 * Q2/3 = # stages ns4/3 ? Δh * ns4/3 = # stages Elev1= the change in elevation head between the two sources. n4/3 * Q2/3 415 [ft] Δh = ytank - ygw

? Find: minimum # of stages = = n4/3 * Q2/3 ns4/3 n4/3 * Q2/3 gal Elev2=825 [ft] Q=500 min n=1,780 [rpm] s=0 [ft] ns>1,500 Δh n4/3 * Q2/3 = # stages ns4/3 ? Δh * ns4/3 = # stages Elev1= Plugging in the given values for elevation, delta h equals, --- n4/3 * Q2/3 415 [ft] Δh = ytank - ygw

Find: minimum # of stages gal Elev2=825 [ft] Q=500 min n=1,780 [rpm] s=0 [ft] ns>1,500 Δh n4/3 * Q2/3 = # stages ns4/3 Δh * ns4/3 = # stages Elev1= 410 feet. [pause] We’re now ready to solve for the minimum number of stages. n4/3 * Q2/3 415 [ft] Δh = ytank – ygw= 410 [ft]

Find: minimum # of stages gal Elev2=825 [ft] Q=500 min n=1,780 [rpm] s=0 [ft] ns>1,500 Δh n4/3 * Q2/3 = # stages ns4/3 Δh * ns4/3 = # stages Elev1= The variables on the right hand side are plugged into the equation, and the number of stages equals, ---- n4/3 * Q2/3 415 [ft] Δh = ytank – ygw= 410 [ft]

Find: minimum # of stages gal Elev2=825 [ft] Q=500 min n=1,780 [rpm] s=0 [ft] ns>1,500 Δh n4/3 * Q2/3 = # stages ns4/3 Δh * ns4/3 = # stages Elev1= 5.18. [pause] Since the problem stated 1,500 is the --- n4/3 * Q2/3 415 [ft] # stages = 5.18 Δh = ytank – ygw= 410 [ft]

Find: minimum # of stages gal Elev2=825 [ft] Q=500 min n=1,780 [rpm] s=0 [ft] ns>1,500 Δh n4/3 * Q2/3 = # stages ns4/3 Δh * ns4/3 = # stages Elev1= minimum specific speed, then 5.18 is the minimum ---- n4/3 * Q2/3 415 [ft] # stages = 5.18 Δh = ytank – ygw= 410 [ft]

Find: minimum # of stages gal Elev2=825 [ft] Q=500 min n=1,780 [rpm] s=0 [ft] ns>1,500 Δh n4/3 * Q2/3 = # stages ns4/3 Δh * ns4/3 = # stages Elev1= number of stages required for the well pump, and is round up to ---- n4/3 * Q2/3 415 [ft] # stages > 5.18 Δh = ytank – ygw= 410 [ft]

Find: minimum # of stages gal Elev2=825 [ft] Q=500 min n=1,780 [rpm] s=0 [ft] ns>1,500 Δh n4/3 * Q2/3 = # stages ns4/3 Δh * ns4/3 = # stages Elev1= 6 stages. n4/3 * Q2/3 415 [ft] # stages > 5.18 # stages = 6 Δh = ytank – ygw= 410 [ft]

Find: minimum # of stages gal Elev2=825 [ft] Q=500 min n=1,780 [rpm] s=0 [ft] ns>1,500 Δh n4/3 * Q2/3 = # stages ns4/3 Δh * ns4/3 = 3 4 5 6 # stages Elev1= When reviewing the possible solutions, --- n4/3 * Q2/3 415 [ft] # stages > 5.18 # stages = 6 Δh = ytank – ygw= 410 [ft]

Find: minimum # of stages gal Elev2=825 [ft] Q=500 min n=1,780 [rpm] s=0 [ft] ns>1,500 Δh n4/3 * Q2/3 = # stages ns4/3 Δh * ns4/3 = 3 4 5 6 # stages Elev1= the answer is D. n4/3 * Q2/3 415 [ft] # stages > 5.18 # stages = 6 Δh = ytank – ygw= 410 [ft] AnswerD

? Index σ’v = Σ γ d γT=100 [lb/ft3] +γclay dclay 1 Find: σ’v at d = 30 feet (1+wc)*γw wc+(1/SG) σ’v = Σ γ d d Sand 10 ft γT=100 [lb/ft3] 100 [lb/ft3] 10 [ft] 20 ft Clay = γsand dsand +γclay dclay A W S V [ft3] W [lb] 40 ft text wc = 37% ? Δh 20 [ft] (5 [cm])2 * π/4