What am i doing wrong (water thru a tube question)

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The discussion revolves around calculating the velocity of water flowing through two connected tubes with different radii. The user is attempting to apply the flow rate equation, Im = v * A, but is struggling with the calculations. Despite converting the flow rate from liters per minute to cubic meters per second, the user consistently arrives at an incorrect velocity. Other participants suggest that the user's mathematical errors stem from improper use of parentheses in their calculations. The conversation emphasizes the importance of careful computation and understanding of the flow rate formula.
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Homework Statement



A tube of radius 6.000 cm is connected to tube of radius 1.000 cm as shown above. (see attachment)..

Water is forced through the tube at a rate of 20.97 liters/min. The pressure in the 6 cm tube is 1.015×105 Pa. The density of water is 1000 kg/m3. Assume that the water is nonviscous and incompressible, and keep at least four digits in your computations.

(a) What is the velocity of the water in the 6 cm radius tube?
this is easy but i keep getting wrong answer --dont know why?

Homework Equations





The Attempt at a Solution


heres what i did
Im = v * A (that is, flow rate = velocvity times area)

so after conversions (20.97l/m /60 * 10^-3 = m^3) i have

Im = 3.495*10^-4m/s * .011 (pie*.06^2)
= 3.845*10^-6m/s

this is wrong.
Why?

please help... thanks!



 

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well i didnt put brackets in right place.
should be
(20.97l/m /60) * 10^-3 = m^3)

=3.495*10^-4

still doesn't solve prob though.
any other help?? please help!??
 
flow rate = velocvity times area
Hence velocity = flow rate/area
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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