Question

one arm of a u shaped tube contains water and the other alcohol. if the two fluids meet exactly at the bottom of the U and the alcohol is at a height of 18 cm at what height will water be

Answer 1

Complete Question

One arm of a U-shaped tube (open at both ends) contains water, and the other alcohol.

If the two fluids meet at exactly the bottom of the U, and the alcohol is at a height of 18 cm, at what height will the water be?Assume the density of alcohol is $\rho_a = 790\ kg/m^3$

Answer:

The  height of water is  $h_w = 0.142 \ m$

Explanation:

From the question we are told that

    The height of the alcohol is  $h_a =18 \ cm = 0.18 \ m$

     The  density of the alcohol is  $\rho_a = 790\ kg/m^3$

Generally the pressure on both arm of the tube are equal given that they are both open

i,e    $P_a = P_w$

Where  $P_a$ is pressure of alcohol and  $P_w$ is pressure of water

   So the pressure on the arm of the tube containing the alcohol is mathematically evaluated as

         $P_a = g * h * \rho$

substituting values

         $P_a =9.8 * 0.18 * 790$

         $P_a = 1394 \ Pa$

Generally the pressure on the arm of the tube containing the water is mathematically evaluated as

       $P_w = g * h_w * \rho_w$

where  $\rho_w$ is the density of water which has  a value $\rho _w = 1000 \ kg/m^3$

So  

      $1394 = 9.8 * h_w * 1000$

=>    $h_w = \frac{1394}{9800}$

=>  $h_w = 0.142 \ m$