Cylindrical water tank is 20.0 m tall, open to the atmosphere at the top, and is filled to the top. It is noticed that a small hole has occurred in the side at a point 16.5 m below the water level and that water is flowing out at the volume flow rate of 2.90 10-3 m3/min. Determine the following. (a) the speed in m/s at which water is ejected from the hole

a

The velocity is  

b

The diameter is  

Explanation:

The diagram of the set up is shown on the first uploaded image  

From the question we are told that

    The height of the water tank is

    The position of the hole below  water level

     The  rate  of water flow

  According to Bernoulli's theorem position of the hole

Where  u is  the initial speed the water through the hole = 0 m/s

              is the atmospheric pressure

Substituting value

The Volumetric flow rate is mathematically represented as

     Making A the subject

 substituting value  

Area is mathematically represented as

  making d the subject

  Substituting values

seeing the graph would

  distance on the y-axis and time on the x-axis.

explanation:

the instantaneous velocity = change in position/time taken

the slope of the graph should give instantaneous velocity.

  slope of a graph = change in value of y -axis / change in values of x -axis

  comparing both the equations

    change in value of y -axis = change in position

  change in values of x -axis = time taken

so position values should be on the y axis and time values should be on the x axis.

distance on the y-axis and time on the x-axis.