Physics help! please. :D

Question

how do you answer this using bernoulli's principle?

thank you.

-If 10 m3 is to be discharged through a pipe in 1 hr, what must be the diameter of the pipe if the velocity of the liquid is 4m/sec?

-A liquid flows through a tube of varying cross-section. If the velocity is 2m/s at the section where the diameter is 10 cm, what is the velocity at the section where the diameter is 20cm?

Answer 1

use ratio method

Answer 2

1) Let area of cross section of the pipe = A

Rate of discharge = Av

10 m3/1 hr = A * 4 m/sec

Or, 10 m3/3600 sec = A * 4 m/sec

Or, A = 10/(3600 * 4) m2 = 6.94 * 10^-4 m2

If diameter is d,

then A = 3.14 * d/2 * d/2 = 3.14 * d2/4

Or, d2 = 4A / 3.14

= 4 * 6.94 * 10^-4 / 3.14

d2 = 8.84 * 10^-4 m2

d = sqrt(8.84 * 10^-4) m

= sqrt(8.84) * 10^-2 m

= 2.97 * 10^-2 m

= 2.97 cm

2) Let u = velocity at first section

v = velocity at second section

x = diameter of first section,

y = diameter of second section

Velocity * Area = constant

Area is proportional to diameter square

Therefore, Velocity * diameter square = const.

Or, u * x2 = v * y2

Or, v = u * x2/y2

= 2 * 10^2/20^2

= 2 * 100/400

=200/400

= 0.5 m/s

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