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Mechanical Properties Of Fluids

Question
CBSEENPH11020321
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Water is flowing continuously from a tap having an internal diameter 8 × 10-3 m. The water velocity as it leaves the tap is 0.4 ms-1. The diameter of the water stream at a distance 2 × 10-1 m below the tap is close
to:

  • 7.5 x 10-3 m

  • 9.6x 10-3 m

  • 3.6x 10-3 m

  • 5.0x 10-3 m

Solution

C.

3.6x 10-3 m

From Bernoulli's theorem
ρgh space equals space 1 half straight rho left parenthesis straight v subscript 2 superscript 2 minus straight v subscript 1 superscript 2 right parenthesis gh space equals space 1 half straight v subscript 1 superscript 2 space open parentheses open parentheses straight v subscript 2 over straight v subscript 1 close parentheses minus 1 close parentheses space left parenthesis therefore straight A subscript 1 straight v subscript 1 space equals straight A subscript 2 straight v subscript 2 right parenthesis rightwards double arrow space space open parentheses straight A subscript 1 over straight A subscript 2 close parentheses squared space equals space 1 space plus space fraction numerator 2 hg over denominator straight v subscript 1 superscript 2 end fraction rightwards double arrow open parentheses straight D subscript 1 over straight D subscript 2 close parentheses to the power of 4 space equals space 1 space plus space fraction numerator 2 gh over denominator straight v subscript 1 superscript 2 end fraction rightwards double arrow space straight D subscript 2 space equals space straight D subscript 1 over open parentheses 1 plus begin display style fraction numerator 2 gh over denominator straight v subscript 1 superscript 2 end fraction end style close parentheses to the power of 1 divided by 4 end exponent space equals space fraction numerator 8 space straight x space 10 to the power of negative 3 end exponent over denominator open parentheses begin display style fraction numerator 1 plus space 2 space straight x space 10 space straight x 0.2 over denominator left parenthesis 0.4 right parenthesis squared end fraction end style close parentheses to the power of 1 divided by 4 end exponent end fraction space equals space 3.6 space straight x space 10 to the power of negative 3 end exponent space straight m

Some More Questions From Mechanical Properties of Fluids Chapter

Why solids have definite shape while liquids do not have definite shape?

What is fluid?

What is hydrostatics?

What is hydrodynamics?

Can fluids withstand tangential stress?

Can fluids withstand normal stress?

Why the fluids do not have any modulus of rigidity?

Which phase of fluid is more compressible?

What is an ideal liquid?

Do liquids exert pressure?

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