Two circular tubes are inserted vertically into a large container filled with liquid that has a surface tension of s = 0.07 N/m, and contact

Question

Two circular tubes are inserted vertically into a large container filled with liquid that has a surface tension of s = 0.07 N/m, and contact angle of q =10 deg. The density of the liquid is 960 kg/m3 the diameter of the first tube is 1.5 mm, and the diameter of the second tube is 2.5 mm. a) calculate how high will the liquid columns rise in each tube. b) Is this in conflict with Pascal’s law?

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Khánh Gia 3 days 2021-07-21T23:30:45+00:00 1 Answers 0 views 0

Answers ( )

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    2021-07-21T23:32:20+00:00

    Answer:

    a

    H_1  =  0.0195 \  m

    H_2  =  0.0117 \  m

    b

    Yes it is in conflict with Pascal’s law

    Explanation:

    From the question we are told that

    The surface tension is s =  0.07 \  N/m

    The contact angle is \theta  =  10^o

    The density is \rho =  960 \  kg/m^3

    The first tube diameter is d_1 =  1.5mm =  1.5 *10^{-3} \  m

    The second tube diameter is d_2 =  2.5mm =  2.5 *10^{-3} \  m

    The first tube radius is r_1 =  \frac{1.5 *10^{-3}}{2}  =  0.75 *10^{-3} \  m

    The first tube radius is r_1 =  \frac{2.5 *10^{-3}}{2}  =  1.5 *10^{-3} \  m

    Generally capillary rise is mathematically represented as

    H  =  \frac{2 * s  *  cos(\theta)}{ \rho * g *  r }

    For first tube

    H_1  =  \frac{2 * 0.07  *  cos(10)}{  960  * 9.8  *  0.75 *10^{-3} }

    H_1  =  0.0195 \  m

    For second tube

    H_2  =  \frac{2 * 0.07  *  cos(10)}{  960  * 9.8  *  1.5 *10^{-3} }

    H_2  =  0.0117 \  m

    From the values obtained we see that

        H_1 \ne H_2

    Which means that Pascal’s law has been violated

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