Problem: Fluids 18, crude oil is pumped by a centrifugal pump with a performance curve given by the equation, had equals 50 minus volume flow rate minus vol...
Given: 000 in 25; 8550 GPM; 16.43 feet
Approach: So first of all, let's think about these two functions, and we'll have to remember a little bit of math here, not too much, jus...
Key formula: equation is Q is going to equal negative B plus our minus the discriminant
Calc: So HP equals HS, let's do our substitution 50 minus Q minus Q squared over 25 equals Q squared over 25 plus Q over 10.
Calc: And now let's get everything on one side equal to 0.
Result: And we get a final answer of 30.5 horsepower, which is closest to answer choice be.
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Student questions asked in live office hours about this problem
OH 120 · May 11, 2026
Q: Can you find the operating point by substituting Q from one curve equation into the other, rather than setting the pump curve and system curve equations equal to each other?
A: The operating point is by definition the intersection of the pump curve and system curve, so you must set the two polynomial expressions equal to each other to find it. This gives you a system of two equations with two unknowns, which you can solve algebraically using substitution, elimination, or a calculator's simultaneous equation solver.