•• Unfiltered olive oil must flow at a minimum speed of 3.0 m/s to prevent settling of debris in a pipe. The oil leaves a pump at a pressure of 88 kPa through a pipe of radius 9.5 mm. It then enters a horizontal pipe at atmospheric pressure. Ignore the effects of viscosity. (a) What is the speed of the oil as it leaves the pump if it flows at 3.0 m/s in the horizontal pipe? (b) What is the radius of the horizontal pipe?

a

The velocity at which the oil leaves the pump is

b

The radius of the horizontal pipe  

Explanation:

From the question we are told that

    The rate of flow of unfiltered olive oil is  

    The pressure on the pump is

     The radius of the pipe is  

Generally we can define this motion with Bernoulli's Equation as

           is the  pressure inside the pipe which is the atmospheric pressure which has a value of

            is the density of olive oil which has a value of

            is the acceleration due to gravity

           h the height of the pipe since from the question we are not told that it is place on anything hence the height is the diameter of the pipe

            are the speed at which it leaves the pump and the speed at which it flows in the pipe respectively

Making  the subject of the equation

Substituting values

Using continuity equation to define the motion of this fluid we have

Where   is the area of the pump which is circular so mathematically it is

          is the area of the horizontal pipe  which is circular so mathematically it is

So the continuity equation becomes

Making subject of formula

Substituting values

6 cos 34, 6 sin 34 trig