According to Oxford Dictionaries, a spit take is an act of suddenly spitting out liquid one is drinking in response to something funny or su

Question

According to Oxford Dictionaries, a spit take is an act of suddenly spitting out liquid one is drinking in response to something funny or surprising. In spit takes, a gauge pressure is applied in the mouth, p1, so that liquid flows through pursed lips forming a column of liquid with radius r2 = 4 mm. If the liquid travels at v2 = 3.1 m/s outside the body, and if the column’s area is 10x larger inside the mouth, what is p1 in Pa?

in progress 0
Hưng Khoa 5 months 2021-08-24T12:44:18+00:00 1 Answers 14 views 0

Answers ( )

    0
    2021-08-24T12:46:14+00:00

    Answer:

    The pressure is p_1 = 4051.4 \ Pa

    Explanation:

    From the question we are told that

         The gauge pressure at the mouth is  p_1

         The radius of the column is  r_2 =  4 \ mm  =  0.004 \ m

        The speed of the liquid outside the body is  v_2 =  3.1 \ m/s

          The area of the column is  A_2

           The area inside the mouth A_1 = 10 A_2

    Generally according to continuity equation

           v_1 A_1 =  v_2 A_2

    =>       v_ 1 = v_2 *  \frac{A_2}{A_1}

    =>      v_ 1 = 3.1 *  \frac{1}{10}

    =>        v_ 1 = 0.31 \ m/s

    So

          A_1 = 10A_2

    =>   \pi * r_1^2 = 10(\pi * r_2^2)

    =>   r_1 = 10 * r_2

    substituting values

            r_1 = 10 * 0.004

            r_1 =0.04 \ m

    Now the height of inside the mouth is  h_1 =  d =  2r_1 =  2* 0.04 =  0.08\ m

    Now the height of the column is  h_2 =  d =  2r_2 =  2* 0.004 =  0.008\ m

    Generally according to Bernoulli’s  equation

            p_1 =  [\frac{1}{2}  \rho v_2^2 + h_2 \rho g +p_2] -[\frac{1}{2} \rho * v_1^2 + h_1 \rho g ]

    Now  \rho =  1000 \ kg m^{-3} which is the density of water

            p_2 is the gauge pressure of the atmosphere which is  zero

     So

           p_1 =  [(0.5 * 1000 * (3.1)^2) +(0.008 * 1000 * 9.8) + 0]-

                                                      [(0.5 * 1000 * 0.31^2) + (0.08*1000 * 9.8)]                          

           p_1 = 4051.4 \ Pa

Leave an answer

Browse

Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )