Solving the Hardy Cross Problem

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The discussion revolves around the Hardy Cross method and the flow rate equation, specifically addressing the equation hf = k(Q^2). There is confusion regarding whether hf should always yield a positive value, given that Q is squared. The user questions why the product (554)(-40^2) results in a negative value when it should be positive due to squaring the flow rate. The inquiry highlights a misunderstanding of how negative values in flow rates affect the overall calculations in the Hardy Cross method. Clarification on this point is sought to resolve the apparent contradiction in the calculations.
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Homework Statement


in this problem , we know that Q (flow rate ) has power of 2 , hf = k(Q^2) , shouldn't the hf = k(Q^2) has positive value ?

Homework Equations

The Attempt at a Solution


since (554)(-40^2) will become positive , same thing goes to hf / Q , when the hf = positive , the hf / Q will become hf / Q divided by Q(has negative value ) , so the hf / Q will have negative value , am i right ?
 

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why will (554)(-40^2) will become negative ?
 
anybody can answer ?
 
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The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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