How to Calculate Flow Rate Using Bernoulli's Equation Without Given Velocity?

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To calculate the flow rate using Bernoulli's Equation without a given velocity, start by applying the equation to the two points in the system, considering the change in gauge pressure of 70.0 kPa. Since the fluid is ideal, the velocities at both cross-sectional areas must be equal, allowing for the use of the equation for volume flow rate, dV/dt = A1v1 = A2v2. The cross-sectional areas are 184 cm² and 45.0 cm², which can be used to express the flow rate in terms of the pressure difference and the areas. By solving for the velocity at each point and substituting back into the flow rate equation, the flow rate can be determined. This method effectively utilizes Bernoulli's principles to find the flow rate in the absence of direct velocity measurements.
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Homework Statement


A horizontal water main with a cross-sectional area of 184 cm2 necks down to a pipe of area 45.0 cm2. Meters mounted in the flow on each side of the transition coupling show a change in gauge pressure of 70.0 kPa. Determine the flow rate through the system, taking the fluid to be ideal.



Homework Equations


p+(1/2)rho*v^2+rho*gy


The Attempt at a Solution


I'm confused about how to do this problem without any velocity given. Thank-you!
 
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You need to solve for flow rate, so I ask, how would you represent flow rate in equation forum? When you apply Bernoulli's Equation, what are your unknowns? What do you know about the flow rate through the system given that the fluid is ideal?
 
set bernoulli's equation equal to zero and solve for v. Now since this is an ideal fluid the velocity of fluid flowing through point a, 1.84m, is going to be equal to the velocity of fluid through point b, 0.45m. So you then use the equation for volume flow rate which is
dV/dt= A1v1= A2v2, where A1 and A2 are the cross-sectional areas at point a and b, respectively.
 

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