Question

Water movinng in a horizontal pipe has a velocity of 9.0 m/s when the radius of the pipe is 0.0025 metr. determine the velocity of the water when it enters a wider section of the pipe and the radius is 0.075 meter.

Please show work

Determine the density of a unkown smaple by using Archemdes Principle and water. the mass measurement of the sample in air is 200 grams, the mass measurement of the sample in water 147 grams.

please show work

Answer 1

1) Mass flow concept

The mass flowing into the pipe = The mass flowing out of the pipe

Definition of mass flow:
mass flow = mass per unit time

Now we use density to define the mass:
density = mass/volume ==> mass = density * volume

Now think of the volume and how we define volume. For simplicity sake we usually define the volume as cross sectional area (A) times unit of length, so Volume = A * unit of length. Plug all that back into our mass flow.

mass flow = A * unit of length per unit of time

What is the basic definition of velocity? A unit of length per unit of time, so

mass flow = A * v

Again, mass flow in = mass flow out

Therefore we can write our mass flow equation as the following:
A1*v1 = A2*v2

Solve for v2:
v2 = A1/A2 * v1

This problem deals with a pipe and a pipe has a circular cross section. What is the area of a circle? Area of circular section = pi*d^2/4

Insert that into our equation:
v2 = (pi*d1^2/4) / (pi*d2^2/4) * v1

Reduce:
v2 = d1^2/d2^2 * v1

Plug in our numbers:
v2 = ((0.0025 cm)^2 / (0.075 cm)^2) * 9 m/s

v2 = 0.01 m/s