Fluid Mechanics & Buoyancy Reviewer

Question and answer flashcards covering key concepts, principles, and practice problems in fluid mechanics and buoyancy.

What determines the pressure exerted at a given depth within a fluid?

Fluid pressure depends strictly on the depth or height of the fluid column ($h$) and the fluid density ($\rho$), expressed as $P = \rho g h$. It does not depend on the container's volume or shape.

Why are interconnected vessels of different shapes and volumes able to hold liquid at the exact same vertical height?

Because water seeks its own level, meaning fluid pressure depends solely on vertical height/depth and not on the vessel's shape or volume.

Why is blood pressure standardly measured on the upper arm?

The upper arm is at the same horizontal height as the heart, ensuring accurate pressure readings unaffected by hydrostatic pressure variations caused by vertical height differences.

What is Pascal's Principle?

Pascal's Principle states that when a force is applied to a confined (enclosed) liquid, the resulting change in pressure is transmitted equally and undiminished to all parts of the fluid and to the container walls ($P_1 = P_2$ or $\frac{F_1}{A_1} = \frac{F_2}{A_2}$).

What is buoyant force ($F_b$)?

Buoyant force is the upward force exerted by a fluid on an object that is partially or completely submerged, balancing out the downward pull of gravity.

What does Archimedes' Principle state?

Archimedes' Principle states that an object partially or completely submerged in a fluid experiences an upward buoyant force equal to the weight of the fluid displaced by the object ($F_b = \rho_{\text{fluid}} \times V_{\text{displaced}} \times g$).

How is Specific Gravity (SG) defined and calculated?

Specific Gravity is a dimensionless ratio comparing the density of a material to the density of pure water ($1000\,\text{kg/m}^3$). It can be calculated as $\text{SG} = \frac{\text{Density}_{\text{object}}}{\text{Density}_{\text{water}}}$ or $\text{SG} = \frac{W_{\text{air}}}{W_{\text{air}} - W_{\text{water}}} = \frac{W_{\text{air}}}{F_b}$.

What is neutral buoyancy?

Neutral buoyancy is the state where an object's overall average density equals the density of the surrounding fluid ($F_b = W$), allowing it to hover suspended at any depth without sinking or floating.

What is the Principle of Flotation?

The Principle of Flotation states that a floating object displaces a weight of fluid equal to its total weight, where the submerged volume fraction equals the density ratio $\frac{V_{\text{submerged}}}{V_{\text{total}}} = \frac{\text{Density}_{\text{object}}}{\text{Density}_{\text{liquid}}}$.

In a hydraulic lift system with a small piston area $A_1 = 0.02\,\text{m}^2$ and a large piston area $A_2 = 0.50\,\text{m}^2$, what pressure is transmitted and what upward force is generated when $F_1 = 400\,\text{N}$ is applied?

The transmitted fluid pressure is $P = \frac{400\,\text{N}}{0.02\,\text{m}^2} = 20,000\,\text{Pa}$ (or $20\,\text{kPa}$), and the upward force generated at the larger piston is $F_2 = 20,000\,\text{Pa} \times 0.50\,\text{m}^2 = 10,000\,\text{N}$.

What is the buoyant force acting on a plastic block completely submerged in water ($\rho = 1000\,\text{kg/m}^3$) if it displaces $0.004\,\text{m}^3$ of water? (Use $g = 9.8\,\text{m/s}^2$)

The buoyant force is $F_b = \rho \times V \times g = 1000\,\text{kg/m}^3 \times 0.004\,\text{m}^3 \times 9.8\,\text{m/s}^2 = 39.2\,\text{N}$ upward.

If a submerged object experiences a buoyant force of $58.8\,\text{N}$ in freshwater ($\rho = 1000\,\text{kg/m}^3$), what volume of water does it displace?

The displaced volume is $V = \frac{F_b}{\rho \times g} = \frac{58.8\,\text{N}}{1000\,\text{kg/m}^3 \times 9.8\,\text{m/s}^2} = 0.006\,\text{m}^3$.

Will a wooden block with a mass of $3.5\,\text{kg}$ float or sink in water ($\rho = 1000\,\text{kg/m}^3$) if its total volume is $0.004\,\text{m}^3$?

The block's weight is $W = 3.5\,\text{kg} \times 9.8\,\text{m/s}^2 = 34.3\,\text{N}$, and its maximum buoyant force is $F_b = 1000\,\text{kg/m}^3 \times 0.004\,\text{m}^3 \times 9.8\,\text{m/s}^2 = 39.2\,\text{N}$. Since $F_b > W$, the block will float to the surface.

What buoyant force acts on an instrument package with volume $V = 0.02\,\text{m}^3$ when fully submerged in seawater ($\rho = 1025\,\text{kg/m}^3$)?

The buoyant force is $F_b = 1025\,\text{kg/m}^3 \times 0.02\,\text{m}^3 \times 9.8\,\text{m/s}^2 = 200.9\,\text{N}$.

What is the specific gravity of a solid coral sample with mass $m = 1.5\,\text{kg}$ that displaces $0.0006\,\text{m}^3$ when submerged in pure water?

The density of the coral sample is $\text{Density}_{\text{object}} = \frac{1.5\,\text{kg}}{0.0006\,\text{m}^3} = 2500\,\text{kg/m}^3$. Its specific gravity is $\text{SG} = \frac{2500\,\text{kg/m}^3}{1000\,\text{kg/m}^3} = 2.50$.

A metal block weighs $90\,\text{N}$ in air and $60\,\text{N}$ when submerged in water. What are the buoyant force and specific gravity of the metal?

The buoyant force is $F_b = 90\,\text{N} - 60\,\text{N} = 30\,\text{N}$, and the specific gravity is $\text{SG} = \frac{W_{\text{air}}}{F_b} = \frac{90\,\text{N}}{30\,\text{N}} = 3.00$.

Why is calculating specific gravity as $\text{SG} = \frac{W_{\text{air}}}{W_{\text{water}}}$ incorrect?

The denominator in the specific gravity formula must represent the weight of the displaced water, which equals the buoyant force ($F_b = W_{\text{air}} - W_{\text{water}}$), not the apparent weight underwater ($W_{\text{water}}$).

What is the density of a wooden statuette of total volume $1250\,\text{cm}^3$ if $937.5\,\text{cm}^3$ remains submerged in pure water ($\rho = 1.00\,\text{g/cm}^3$)?

The density is $\text{Density}_{\text{object}} = 1.00\,\text{g/cm}^3 \times \left(\frac{937.5\,\text{cm}^3}{1250\,\text{cm}^3}\right) = 0.75\,\text{g/cm}^3$, which matches typical oak timber.

If an iceberg made of ice ($\rho = 917\,\text{kg/m}^3$) floats in seawater ($\rho = 1025\,\text{kg/m}^3$) and has an exposed volume above water of $1296\,\text{m}^3$, what is its total volume?

The fraction submerged is $\frac{917}{1025} \approx 0.8946$ ($89.46\%$), making the exposed fraction $1 - 0.8946 = 0.1054$ ($10.54\%$). The total volume is $V_{\text{total}} = \frac{1296\,\text{m}^3}{0.1054} \approx 12,296.02\,\text{m}^3$.

For a composite buoy with total volume $V_{\text{total}} = 0.85\,\text{m}^3$ and mass $m = 697\,\text{kg}$, what is its average density, submerged volume in freshwater, and percentage submerged in seawater ($\rho = 1025\,\text{kg/m}^3$)?

Its average density is $\rho_{\text{object}} = \frac{697\,\text{kg}}{0.85\,\text{m}^3} = 820.00\,\text{kg/m}^3$. In freshwater ($1000\,\text{kg/m}^3$), its submerged volume is $0.85\,\text{m}^3 \times 0.82 = 0.697\,\text{m}^3$ (or $0.70\,\text{m}^3$). In seawater, it is $\left(\frac{820.00}{1025}\right) \times 100\% = 80.00\%$ submerged, with $0.17\,\text{m}^3$ sticking out.