Fluids bernoulli's equation problem

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In a horizontal tube system with differing diameters, the larger tube (2.8 cm) has a higher pressure and lower fluid speed, while the smaller tube (1.6 cm) exhibits higher fluid speed and lower pressure. The pressure difference of 7.5 kPa indicates that the fluid accelerates as it moves into the smaller diameter tube, resulting in increased velocity. To analyze the flow quantitatively, one can use Bernoulli's equation by substituting dummy variables for pressures in each tube. By establishing relationships between pressure and speed, it becomes possible to solve for the unknown velocities in both tubes. Understanding these principles allows for a comprehensive analysis of fluid dynamics in varying tube diameters.
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Water flows throgh a horizontal tube of diameter 2.8cm that is joined to a second horizontal tube of diameter 1.6cm. the pressure difference between the tubes is 7.5kPa. which tube has the higher pressure flow? which tube has the higher speed flow? find the speed of flow in the first tube.

P2=p1+ (1/2)density(rho)(v1^2-v2^2)

how can i solve without a velocity 1 or 2?
 
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Without worrying about numbers (quantitative parts) -- can you first answer the qualitative parts?
 
pressure is greater in the bigger area with less fluid speed. the greater fluid speed has the least pressure.
 
Okay -- now say you KNOW the pressure in each part -- just call them dummy variables say P_b and P_s for the big and small diameter tubes. Can you then individually know the speeds in the tubes as functions of P_b and P_s? then you know the difference between P_b and P_s. Try setting up those... Then you might have as many equations as unknowns ands be able to solve for all your unknowns, including the velocity you want.
 

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