Problem 23 - Physics

Question

Some researchers believe that the dinosaur Barosaurus held its head erect on a long neck, much as a giraffe does. If so, fossil remains indicate that its heart would have been about \(12 \mathrm{~m}\) below its brain. Assume that the blood has the density of water, and calculate the amount by which the blood pressure in the heart would have exceeded that in the brain. Size estimates for the single heart needed to withstand such a pressure range up to two tons. Alternatively, Barosaurus may have had a number of smaller hearts.

Step-by-Step Solution

Answer

The blood pressure difference is 117,600 Pa.

Step 1: Understanding the Problem

We need to calculate the difference in blood pressure between the heart and the brain of a Barosaurus. The height difference between the heart and the brain is given as 12 meters.

Step 2: Identify Relevant Physics Principles

The pressure difference due to a height difference in a fluid is given by the equation for hydrostatic pressure: \ \( \Delta P = \rho g h \ \), where \( \rho \) is the fluid density, \( g \) is the acceleration due to gravity, and \( h \) is the height difference.

Step 3: Input Values and Constants

The density \( \rho \) of blood is approximated as the density of water, \( 1000 \, \text{kg/m}^3 \). The acceleration due to gravity \( g \) is approximately \( 9.8 \, \text{m/s}^2 \). The height difference \( h \) is \( 12 \, \text{m} \).

Step 4: Calculate Pressure Difference

Plug the values into the hydrostatic pressure formula: \[\Delta P = (1000 \, \text{kg/m}^3)(9.8 \, \text{m/s}^2)(12 \, \text{m})\]Calculate to find:\[\Delta P = 117600 \, \text{N/m}^2 \text{ or } 117600 \, \text{Pa}\].

Step 5: Conclusion and Result

The blood pressure in the heart would exceed that in the brain by \( 117600 \, \text{Pa} \). This high pressure might necessitate a powerful heart or multiple hearts.

Key Concepts

Barosaurus

Barosaurus was a giant dinosaur that lived approximately 150 million years ago. Much like the giraffe of today, some scientists believe that Barosaurus held its head erect on a very long neck. Imagine carrying your head atop a neck that could be as long as 12 meters. This unique physical trait presents interesting challenges, especially when it comes to pumping blood from the heart all the way up to the head. Such a long neck means the heart must work super hard to push blood against gravity, requiring either an extraordinarily large heart or perhaps several smaller hearts distributed along its body. This is purely speculative, but it gives us insight into the fascinating adaptations of these creatures.

Fluid Dynamics

Fluid dynamics is the study of how fluids - like liquids and gases - move and interact. It's a branch of physics that helps us understand things like water flow in rivers, the way air circulates around a plane, or even how blood circulates within the body. In the case of Barosaurus, fluid dynamics comes into play when considering how the blood would travel from its heart to its brain.

• First, since blood behaves like a fluid, it follows the principles of fluid dynamics, which involves understanding how pressure, density, and velocity interact.
• Second, in the case of a dinosaur like Barosaurus, the pressure difference due to its height becomes a critical factor in efficiently moving the blood.

Understanding these principles is crucial in biology and medicine, as it influences how we study cardiovascular systems in both ancient and modern animals.

Blood Density

Blood density is an important factor when calculating pressure differences in fluid systems. In physics, the density of a fluid like blood can be thought of as its mass per unit volume, usually expressed in kilograms per cubic meter. For simplification in many calculations, the density of blood is often approximated as the density of water, which is about 1000 kg/m³.
So, when considering Barosaurus, we use this water density approximation to calculate how much pressure the heart must exert to push blood up through the neck. This approximation simplifies the math while still providing useful insight into the biological challenge these dinosaurs faced. Next time you think about blood coursing through your veins, remember similar principles might have helped the Barosaurus keep its brain oxygenated too.

Pressure Calculation

Pressure calculation in fluids is a vital concept often represented by the hydrostatic pressure equation: \( \Delta P = \rho g h \). This equation shows that pressure difference (\( \Delta P \)) is the product of the fluid's density (\( \rho \)), gravitational acceleration (\( g \)), and the height difference (\( h \)).

• For Barosaurus, given the height difference between heart and brain is 12 meters, and using the density of water for blood, the pressure difference is calculated to be 117600 Pa.
• It's important to grasp that the blood pressure at the heart needs to be significantly higher to move blood up through the long neck to the brain.

This knowledge of pressure calculations is not only crucial for understanding the circulatory requirements of extinct creatures like dinosaurs but is also applicable to various engineering and medical practices today.