Suppose that two tanks, 1 and 2, each with a large opening at the top, contain d

Question

Suppose that two tanks, 1 and 2, each with a large opening at the top, contain different liquids. A small hole is made in the side of each tank at the same depth 1.72 m below the liquid surface, but the hole in tank 2 has 1.76 times the cross-sectional area of the hole in tank 1. (a) What is the ratio 1/2 of the densities of the liquids if the mass flow rate is the same for the two holes? (b) What is the ratio RV1/RV2 of the volume flow rates from the two tanks? (c) At one instant, the liquid in tank 1 is 12.1 cm above the hole. If the tanks are to have equal volume flow rates, what height above the hole must the liquid in tank 2 be just then?

The answers I got were:

a) 1.13 (Wrong)

b) .569 (correct)

c) 3.02cm (wrong)

I need help on a and c please!

Explanation / Answer

from the given data,

v1 = v2

A2 = 1.76*A1

a) mass flow rate is same

so,

rho1*A1*v1 = rho*A2*v2

rho1/rho2 = A2/A1

= 1.76*A1/A1

= 1.76 <<<<<<<<<-----------Answer

b) ratio of volume flow rates = A1*v1/(A2*v2)

= rho2/rho1

= 1/1.76

= 0.568 <<<<<<<<<-----------Answer

c) A1*v1 = A2*v2

v2 = A1*v1/A2

sqrt(2*g*h2) = A1*sqrt(2*g*h1)/(1.76*A1)

h2 = h1/1.76^2

= 12.1/1.76^2

= 3.91 cm <<<<<<<<<-----------Answer

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