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 13 m below its brain. Assume that the blood has the denisty 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 need to withstand such a pressure range up to two tons. Alternatively, Barosaurus may have had a number of smaller hearts.
What is the weight of a column of water 13m high? Assume some area A.
Pressure= weight/A
To calculate the pressure difference between the heart and the brain of Barosaurus, we need to use the equation for pressure:
Pressure = Density x Gravity x Height
Given that the density of blood is approximately the same as water (1000 kg/m³) and the acceleration due to gravity is 9.8 m/s², we can calculate the pressure at the heart and the brain.
1. Pressure at the heart:
Using the given information, the distance between the heart and the brain is 13 meters. So, the pressure at the heart is:
Pressure_h = Density x Gravity x Height_h
= 1000 kg/m³ x 9.8 m/s² x 13 m
= 127,400 Pa
2. Pressure at the brain:
Since the brain is at a higher level, the pressure at the brain would be lower. We need to calculate the height difference between the heart and the brain.
Height_diff = Height_h - Height_brain
= 13 m - 0 m (assuming the brain is at ground level)
= 13 m
Now we can calculate the pressure at the brain:
Pressure_brain = Density x Gravity x Height_brain
= 1000 kg/m³ x 9.8 m/s² x 0 m
= 0 Pa
Therefore, the pressure difference between the heart and the brain is:
Pressure_difference = Pressure_h - Pressure_brain
= 127,400 Pa - 0 Pa
= 127,400 Pa
To estimate the force exerted on the heart, we can multiply the pressure difference by the area of the heart's surface. However, we would need additional information to determine the exact surface area and calculate the force. The given information suggests that the heart needs to withstand pressure up to two tons, but we cannot provide a precise calculation without further details.
Alternatively, the idea of having multiple smaller hearts in Barosaurus is a hypothesis and would require more evidence or research to determine its validity and how it would affect the pressure difference.
To calculate the amount by which the blood pressure in the heart of Barosaurus would have exceeded that in the brain, we can use the concept of hydrostatic pressure.
Hydrostatic pressure is the force exerted by a fluid due to its weight. We can calculate the pressure difference between the heart and the brain by comparing the vertical distance between them and the density of the fluid, which in this case is the density of blood (assumed to be equivalent to the density of water).
First, let's convert the vertical distance between the heart and brain into meters:
13 m
Now, let's calculate the pressure difference. The pressure at any point in a fluid column is given by the equation:
Pressure (P) = density (ρ) * gravitational acceleration (g) * height (h)
Density of blood (ρ) ≈ density of water ≈ 1000 kg/m^3 (assuming standard conditions)
Gravitational acceleration (g) ≈ 9.8 m/s^2
Using these values, we can calculate the pressure at the heart and the brain:
Pressure at heart = 1000 * 9.8 * 13
Pressure at brain = 1000 * 9.8 * 0
Pressure at heart ≈ 127,400 Pa (Pascal)
Pressure at brain ≈ 0 Pa (Pascal)
The pressure difference between the heart and the brain would be:
Pressure difference = Pressure at heart - Pressure at brain
Pressure difference ≈ 127,400 Pa - 0 Pa
Pressure difference ≈ 127,400 Pa
Now, let's convert the pressure difference into tons. We know that 1 ton is equivalent to 9.8 x 10^3 N (Newton).
Pressure difference in tons = Pressure difference / (9.8 x 10^3 N)
Pressure difference in tons ≈ 127,400 Pa / (9.8 x 10^3 N)
Pressure difference in tons ≈ 13 tons
So, the blood pressure in the heart of Barosaurus would have exceeded that in the brain by approximately 13 tons.
As for the size estimates and the consideration of multiple smaller hearts, that would require further research and analysis as it involves anatomical and physiological aspects that go beyond the simple pressure calculation.