## MCAT Physics and Math Review

## Chapter 4: Fluids

### Conclusion

The behavior of fluids impacts every moment of our lives. Even if we are nowhere near an ocean or a lake, we are quite literally submerged in a vast expanse of fluid, a mix of gases known as the atmosphere, which exerts forces on all of the surfaces of our bodies. Whenever we take a bath or submerge an object in water, we experience the effect of buoyant forces exerted by the displaced fluid. When we water our gardens, take a shower, or ride in a car with open windows, we experience the speeds, forces, and pressures of a fluid on the move. In the world of medicine, one must consider fluids, flowing and at rest, when evaluating the function of the respiratory and circulatory systems: conditions as varied as asthma and heart murmurs are related to the way in which the body causes fluids to flow. The balance of hydrostatic and oncotic pressures is important for maintaining the proper balance of fluid in the peripheral tissues of the body.

Now that you have the basic concepts of hydrostatics and fluid dynamics, learn to apply them to MCAT passages and questions through your Kaplan practice materials. Don’t be intimidated by the seeming complexity of buoyant force problems and applications of Bernoulli’s equation. Remember that all fluids, whether liquid or gas, exert buoyant forces against objects that are placed in them as a function of the weight of the fluid displaced. Remember that incompressible fluids demonstrate an inverse relationship between their dynamic pressure (as a function of speed) and their static pressure. This chapter concludes the section of this book focusing on mechanics; in the next two chapters, we’ll turn our attention to electrostatics and electricity.

### Concept Summary

*Characteristics of Fluids and Solids*

· **Fluids** are substances that have the ability to flow and conform to the shape of their containers.

o Fluids can exert perpendicular forces, but cannot withstand shear forces.

o Liquids and gases are the two phases of matter that are fluids.

· **Solids** do not flow and they retain their shape regardless of their containers.

· **Density** is the mass per unit volume of a substance (fluid or solid).

· **Pressure** is defined as a measure of force per unit area; it is exerted by a fluid on the walls of its container and on objects placed in the fluid.

o It is a scalar quantity; its value has magnitude only, and no direction.

o The pressure exerted by a gas against the walls of its container will always be perpendicular (normal) to the container walls.

· **Absolute pressure** is the sum of all pressures at a certain point within a fluid; it is equal to the pressure at the surface of the fluid (usually atmospheric pressure) plus the pressure due to the fluid itself.

· **Gauge pressure** is the name for the difference between absolute pressure and atmospheric pressure. In liquids, gauge pressure is caused by the weight of the liquid above the point of measurement.

*Hydrostatics*

· **Pascal’s principle** states that an applied pressure to an incompressible fluid will be distributed undiminished throughout the entire volume of the fluid

· **Hydraulic machines** operate based on the application of Pascal’s principle to generate mechanical advantage.

· **Archimedes’ principle** governs the buoyant force. When an object is placed in a fluid, the fluid generates a** buoyant force** against the object that is equal to the weight of the fluid displaced by the object.

o The direction of the buoyant force is always opposite to the direction of gravity.

o If the maximum buoyant force is larger than the force of gravity on the object, the object will float. This will be true if the object is less dense than the fluid it is in.

o If the maximum buoyant force is smaller than the force of gravity on the object, the object will sink. This will be true if the object is more dense than the fluid it is in.

· Fluids experience **cohesive** forces with other molecules of the same fluid and** adhesive** forces with other materials; cohesive forces give rise to **surface** **tension**.

*Fluid Dynamics*

· Fluid dynamics is a set of principles regarding actively flowing fluids.

· **Viscosity** is a measurement of a fluid’s internal friction. **Viscous drag** is a nonconservative force generated by viscosity.

· Fluids can move with either **laminar flow** or **turbulent flow**.

o The rate of laminar flow is determined by the relationships in **Poiseuille’s law**.

o On the MCAT, incompressible fluids are assumed to have laminar flow and very low viscosity while flowing, allowing us to assume conservation of energy.

· The **continuity equation** is a statement of the conservation of mass as applied to fluid dynamics.

· **Bernoulli’s equation** is an expression of conservation of energy for a flowing fluid. This equation states that the sum of the **static pressure** and the **dynamic pressure** will be constant between any two points in a closed system.

· For a horizontal flow, there is an inverse relationship between pressure and speed, and in a closed system, there is a direct relationship between cross-sectional area and pressure exerted on the walls of the tube known as the **Venturi effect**.

*Fluids in Physiology*

· The circulatory system behaves as a closed system with nonconstant flow.

· Resistance decreases as the total cross-sectional area increases.

o Arterial circulation is primarily motivated by the heart.

o Venous circulation has three times the volume of arterial circulation and is motivated by the skeletal musculature and expansion of the heart.

· Inspiration and expiration create a pressure gradient not only for the respiratory system, but for the circulatory system as well.

· Air at the alveoli has essentially zero speed.

Answers to Concept Checks

· **4.1**

1. Gauge pressure is equal to the pressure exerted by a column of fluid plus the ambient pressure above the fluid, minus atmospheric pressure. When atmospheric pressure is the only pressure above the fluid column, then gauge pressure equals the fluid pressure.

2. Weight is density times volume and acceleration due to gravity.

3. The SI unit of pressure is the pascal. Other common units include mmHg, torr, and atm.

4. True. Density is directionless, and is thus a scalar quantity.

· **4.2**

1. Cohesion is the attractive force experienced by molecules of a fluid for one another. Adhesion is the attractive force experienced by molecules of a fluid for a different material (usually a solid).

2. If adhesive and cohesive forces are equal, then no meniscus would form and the liquid surface would be flat.

3. The displaced volume is equal to the volume of the block. The buoyant force is equal to the weight of the block, and is equal to the weight of the displaced fluid. By extension, the block and the fluid in which it is immersed must have the same density.

4. False. A fluid with a low specific gravity can be used instead of water to determine volumes of objects that would otherwise float in water.

5. The operator usually applies a force to the side with the smaller cross-sectional area. Because pressure is the same on both sides of the lift, a smaller force can be applied on the smaller surface area to generate the desired pressure.

· **4.3**

1. Dynamic pressure is the pressure associated with flow, and is represented by Static pressure is the pressure associated with position; static pressure is sacrificed for dynamic pressure during flow. A pitot tube is a device that measures static pressure during flow to calculate speed. Viscosity is a measure of the resistance of a liquid to flow. Laminar flow is flow in which there are no eddies and in which streamlines roughly parallel each other. Turbulence is the presence of backflow or current eddies.

2. The continuity equation describes the relationship of flow and cross-sectional area in a tube, while Bernoulli’s equation describes the relationship between height, pressure, and flow. The Venturi effect is the direct relationship between cross-sectional area and pressure, and results from the combined relationships of the Bernoulli and continuity equations.

3. Flow rate depends on the radius of the tube, pressure gradient, viscosity, and length of the tube.

· **4.4**

1. The continuity equation cannot be applied to human circulation. The presence of pulses, the elasticity of the vessels, and the nature of the pressure gradient preclude this type of analysis. Poiseuille’s law should instead be used for isolated segments.

2. Total resistance increases as the air exits the body despite the increase in the diameter of the airways. This is because there are fewer airways in parallel with each other.

3. In theory, there should be equal flow in the venae cavae and the main pulmonary trunk. In reality, the flow in the venae cavae is actually slightly less than in the pulmonary trunk because some of the blood entering the right side of the heart is actually from cardiac (coronary) circulation, not systemic circulation.

### Equations to Remember

(4.1) **Density**:

(4.2) **Weight of a volume of fluid**: **F**_{g} = *ρV***g**

(4.3) **Specific gravity**:

(4.4) **Pressure**:

(4.5) **Absolute pressure**: *P* = *P*_{o} **+** *ρ*g*z*

(4.6) **Gauge pressure**:

*P*_{gauge} = *P* – *P*_{atm} = (*P*_{o} + *ρ*g*z*) – *P*_{atm}

(4.7) **Pascal’s principle**:

(4.8) **Buoyant force**:

*F*_{buoy} = *ρ*_{fluid}*V*_{fluid} _{displaced}g = *ρ*_{fluid}*V*_{submerged}g

(4.9) **Poiseuille’s law**:

(4.10) **Critical speed**:

(4.11) **Continuity equation**: *Q* = *ν*_{1}*A*_{1} = *ν*_{2}*A*_{2}

(4.12) **Bernoulli’s equation**:

### Shared Concepts

· **Biology Chapter 6**

o The Respiratory System

· **Biology Chapter 7**

o The Cardiovascular System

· **Biology Chapter 8**

o The Immune System

· **General Chemistry Chapter 8**

o The Gas Phase

· **Physics and Math Chapter 2**

o Work and Energy

· **Physics and Math Chapter 3**

o Thermodynamics