Fluids (major modifications in handout)
|
Format for All Lab Reports (use for parts 1 and 3 below) |
|
Archimedes’ Principle states that the buoyant
force on a submerged object is equal to the weight of the fluid that
is displaced by the object. An object displaces an amount of fluid equal to its own volume, so the weight of the displaced fluid, i.e., the buoyant force on an object is given by the weight of the fluid displaced. Lab Description
The object that you will submerge in water is a right circular cone. Calculate the volume of the object. From knowing the volume of the object, estimate the buoyant force. Using a force spring to support the object while it is submerged in water, compare the actual buoyant force with the “calculated” buoyant force.
a. What happens if you submerge the weighted cylinder in oil instead of water?
b. How does the buoyant force change?
c. Is there is a buoyant force on all objects submerged in a fluid.
d. Is there a buoyant force on you? If so, what is it? |
 |
| The scale to be used and
the object are shown on the right below. On the left is a drawing of
the frustrum of a right circular cone (the shape of the object.
This is the shape of the object that you will use in the Archimedes
portion of the lab Frustrum of a right circular cone A right cone is one whose axis is perpendicular to the plane containing its base A circular cone is one whose base is a circle. The frustrum of a cone is formed by removing a portion of the top by slicing it with a plane that is parallel to the base. The volume, V, of a right circular cone is calculated as shown below Volume of a right circular cone = (1/3)ph(R12 + R22 + R1R2)1/2 |
||
 |
 |
|
Requirements
Weigh the object before being immersed in the liquid (water) and then after it is submerged.
Explain any differences, if any.
Answer questions a through d above.
|
Bernoulli was a Dutch-Swiss mathematician, who is particularly remembered for his applications of mathematics to mechanics, especially fluid mechanics, and for his pioneering work in probability and statistics.
Bernoulli contributed to many scientific fields, but in physics his contribution to the field of aeronautics earned him widespread respect.
Bernoulli’s equation is analogous to our energy conservation equation.
In fact, if one multiplies Bernoulli’s equation through by V, volume, the equation would be conservation of mechanical energy.
Bernoulli's Equation: P + rgh + 1/2rv2 = constant, in the absence of turbulence and frictional effects.
Torricelli's Equation can be derived from Bernoulli, with 2 assumptions:
(1) Both top and the exit are open to the atmosphere
(2) The hole radius is much smaller than the tank radius. |
 |
|
Lab Description
We will use a container with 3 holes (equal radius) in it.
The holes are different distances from the top of the liquid (water)
Another container will be used to maintain a consistent water height in the spout container. The spout container will be used to predict and measure the horizontal displacement of the water than is ejected from various spouts on the side of the container.
Using Bernoulli’s equation, you can estimate the velocity of the water as it leaves the hole. Once the water leaves the hole, it is in free fall and you can use the equations for constant acceleration in the x & y dimensions, to estimate the horizontal displacement of the water.
Be sure the water completely fills the pail before each experiment. |
 |
Requirements
1. Predict and measure
a. Predict, and then measure the horizontal displacement of the fluid from each hole.
Ensure that you keep the level of the water in the “spout container” constant.
b. Explain any discrepancies between Bernoulli predictions (see my derivation) and those of Torricelli
2. Maximum displacement
a. Where should you bore a hole to obtain the maximum velocity
b. Why?
Part 3: Bernoulli and Torricelli
| The pail
on the right has two holes in it. They are the same distance from the top of the water but they have different radii. Observe the distances the water reaches from each of the two holes (can be done simultaneously because of the placement). Explain any differences in the distances (and, hence, velocities). You do not need to perform any calculations or place this part in a lab format. I will demonstrate the experiment; observe and respond to the above. |
 |