Fluid Mechanics Lab Report

Contents

Objective3

Theory3

Experimental Method4

Equipment needed for this experiment4

Procedure4

Results5

Discussion of Results6

Sources of errors8

Conclusions8

References8

Objective

The objective of performing this experiment is to measure the hydrostatic force on a partially submerged vertical surface and to compare the force found in the experiment to the theoretical equivalents. Theory

A submerged body will experience a hydrostatic force due to the weight of the fluid above it as indicated in the figure below:

The magnitude of the resultant force (Fh) is the product of the pressure at the centroid (ρgy) and the surface area (A). The line of action of this force (Yp) is at a distance (Yc) below the centroid (y). For a vertical surface, it can be shown that:

y=h2 Yc=h6 Yp=y+Yc

∴Yp=2h3

Experimental Method

Equipment needed for this experiment

As indicated in the diagram below a partially submerged dam wall is connected to a crossbeam that pivots on a fulcrum above the water tank. The crossbeam also extends at a distance perpendicular to the dam surface. This lever arm can be loaded with different weights: thus creating an effective balance with the hydrostatic load. The tank has an attached device used to measure the amount of water in the tank in millimeters (mm). A spirit-level on the lever arm indicates when the lever is balanced horizontally.

Free body diagram of apparatus:

Procedure

1. Assemble test device.

2. Adjust the weight balance to level arm by means of the adjustable end weight. 3. Add a weight of 20g to the weight tray and fill tank with water until the crossbeam is balanced. Note result. 4. Increase weight in the tray by 20g increments and note the corresponding water level required to re-balance the crossbeam. Repeat until 200g of weight has been used.

Results

Mass (kg)| Weight (N)| Water height (m)|

0| 0| 0|

0.02| 0.1962| 0.0295|

0.04| 0.3924| 0.042|

0.06| 0.5886| 0.051|

0.08| 0.7848| 0.06|

0.1| 0.981| 0.0665|

0.12| 1.1772| 0.074|

0.14| 1.3734| 0.08|

0.16| 1.5696| 0.086|

0.18| 1.7658| 0.0916|

0.2| 1.962| 0.097|

Example of the hydrostatic force (Fh) equation being used:

Fh=ρgyAρ=1000kg/m3

g=9.81m/s2

Fh=10009.81(0.0485)(0.0295x0.075)y=0.0485m

A=Area

∴Fh=1.05N

Equation used to find L2 as well as an example:

L2=L3-13hL3=0.2m

h=0.097m

L2=0.2-130.097

∴L2=0.17m

Equation used to find the Experimental Hydrostatic force (FHex) and an example:

FHex=WL1L2W=Weight

L1=0.3m

FHex=0.19620.30.17L2=0.17m

∴FHex=0.35N

Using the above methods, I worked out the Hydrostatic force for each of the measurements and created a table showing the answers.

Mass (kg)| Weight (N)| Water height (m)| Fh (Theoretical) in (N)| L2 in (m)| Fh (Experimental) in (N)| 0| 0| 0| 0| 0| 0|

0.02| 0.1962| 0.0295| 1.05| 0.17| 0.35|

0.04| 0.3924| 0.042| 1.5| 0.17| 0.69|

0.06| 0.5886| 0.051| 1.82| 0.17| 1.04|

0.08| 0.7848| 0.06| 2.14| 0.17| 1.38|

0.1| 0.981| 0.0665| 2.37| 0.17| 1.73|

0.12| 1.1772| 0.074| 2.64| 0.17| 2.08|

0.14| 1.3734| 0.08| 2.85| 0.17| 2.42|

0.16| 1.5696| 0.086| 3.07| 0.17| 2.77|

0.18| 1.7658| 0.0916| 3.27| 0.17| 3.12|

0.2| 1.962| 0.097| 3.46| 0.17| 3.46|

Discussion of Results

To fully understand the results we need to create a graph representing Fh vs. h as well as a graph showing the difference between Fh and FHex vs. h.

So as the water level increases, we find that the hydrostatic force also increases. The graph line is not linear so I have included a line of best fit so that a more linear set of values can be obtained. I have also made an analysis of error on the graph by using Standard Error to show the degree of error that...