**Problem Statement:**At a given instant, the blood pressure in the heart is \(1.7 \times 10^4 \, \text{Pa}\). If an artery in the brain is 0.46 m above the heart, what is the pressure in the artery? Ignore any pressure changes due to blood flow.**Discussion:**In this problem, we are asked to determine the pressure within an artery in the brain given the pressure at the heart and the vertical distance between the heart and the brain. We are to disregard any pressure changes attributable to the dynamic flow of blood, implying that we should focus on the hydrostatic pressure difference.**Key Concepts:**1. **Pascal's Principle:** When dealing with fluids at rest (hydrostatics), the pressure change in an incompressible, static fluid is given by the hydrostatic pressure equation: \[ P_2 = P_1 + \rho g h \] Where: - \( P_2 \) is the pressure at the point in question (artery in the brain). - \( P_1 \) is the initial pressure (pressure in the heart). - \( \rho \) is the density of the blood (assumed to be 1060 kg/m³). - \( g \) is the acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \)). - \( h \) is the height difference (0.46 m in this case).2. **Hydrostatic Pressure Calculation:** The difference in heights within a vertical column of fluid results in a difference in pressure between the top and the bottom: \[ \Delta P = \rho g h \]**Application to the Problem:**Given:- The pressure in the heart, \( P_1 = 1.7 \times 10^4 \, \text{Pa} \)- The height difference, \( h = 0.46 \, \text{m} \)- The density of blood, \( \rho = 1060 \, \text{kg/m}^3 \)- The acceleration due to gravity, \( g = 9.81 \, \text{m/s}^2 \)We need to find the new pressure \( P_2 \) in the artery located in the brain.First, calculate the

Name: **Problem Statement:**At a given instant, the blood pressure in the h
Uploaded: 2024-03-20T06:51:10.000Z
Channel: Bartleby
Description: **Problem Statement:**At a given instant, the blood pressure in the heart is \(1.7 \times 10^4 \, \text{Pa}\). If an artery in the brain is 0.46 m above the heart, what is the pressure in the artery? Ignore any pressure changes due to blood flow.**D

Here Blood pressure in the heart = P1 = 1.7 × 104 PaWe have to calculate the blood pressure in the…

Science

Physics

At a given instant, the blood pressure in the heart is 1.7 x 104 Pa. If an artery in the brain is 0.46 m above the heart, what is the pressure in the artery? Ignore any pressure changes due to blood flow.

At a given instant, the blood pressure in the heart is 1.7 x 104 Pa. If an artery in the brain is 0.46 m above the heart, what is the pressure in the artery? Ignore any pressure changes due to blood flow.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Related questions

Q: The top of your head is about 30 cmcm above your heart. What is the blood pressure difference…

Q: A mercury barometer is an instrument in which the weight of a column of mercury in a glass tube with…

Q: An airplane is in level flight at low altitude, so that atmospheric pressure and densities are 1 atm…

Q: A large man sits on a four-legged chair with his feet off the floor. The combined mass of the man…

Q: A tank holds a large amount of water. A pipe is connected to the tank at the upper end and is open…

A: Bernoulli's equation is P+12ρv2+ρgh=constant…

Q: Scuba divers are admonished not to rise faster than their air bubbles when rising to the surface.…

Q: In order to draw air into your lungs, your diaphragm and other muscles contract, increasing the lung…

A: in this question we use equation of state of gas.

Q: A swimming pool has a depth of 10 m and is filled with salt water with density 1.03 x 10^3 kg/m3.…

A: Depth of swimming pool h = 10 m Density ρ = 1.03×105 kg/m³ Atmospheric pressure Patm = 1.013×105 Pa…

Q: Normal atmospheric pressure at location A is 1.010 x 105 Pa. During a storm, the mercury column…

A: The barometric formula is givenWhere: is the final atmospheric pressure. is the initial atmospheric…

Q: A 1.50 mL syringe has an inner diameter of 5.00 mm, a needle inner diameter of 0.260 mm, and a…

Q: Smoking tobacco is bad for your circulatory health. In an attempt to maintain the blood’s capacity…

A: Given data: The pressure difference between two ends of an artery for a non-smoker is: ∆P1 = 8 mm of…

Q: A plastic tube has an inner diameter of d = 13.4 mm, and it can withstand a gauge pressure of Pmax =…

A: Here's how to solve it:* *Step 1: Identify the relevant forces.*There are two main forces acting on…

Q: The pressure in the atmosphere is not a constant but fluctuates as the weather changes. If the…

A: The pressure difference is 7.3% atm or 0.073 atm. Now 1 atm=1.013×105 Pa=1.013×105 N/m2 Hence the…

Q: The blood pressure in your heart is 1.71 x104 Pa. If an artery in the brain is 0.534 m above the…

Q: The drawing shows an intravenous feeding. With the distance shown, nutrient solution (p = 1020…

A: Given, nutrient solution density = 1020 kg/m3 height h = 0.610 m Now, the gauge pressure…

Q: A uniform pressure of 7.0x105 Pa is applied to all six sides of a copper cube. What is the…

Q: A 1 cm long section of a blood vessel has a constriction that reduces the inner diameter from 4 mm…

Q: A certain rigid aluminum container contains a liquid at a gauge pressure equal to P0 = 2.02 × 105 Pa…

Q: The four tires of an automobile are inflated to a gauge pressure of 1.7 X 10 Each tire has an area…

A: Given that Gauge pressure(P) = 1.7×105Pa Area (A) = 0.027m2

Q: Pressure is defined by many units. The most common are based on measuring the length of mercury in…

A: Pressure is defined as force applied on the surface per unit area of the surface. Mathematically, P…

Q: Water at ground level is moving at a speed of 1.20 m/sec in a pipe at a pressure of 950 kPa. The…

A: Given : Pressure on the ground floor, P1 = 950 kPa Height of the fourth floor from the ground, h2 =…

Q: The atmospheric pressure above a swimming pool changes from 745 to 764 mm of mercury. The bottom of…

Q: Concrete is pumped from a cement mixer to the place it is being laid, instead of being carried in…

A: Consider the given data as below. The flow rate is, Q=220 Lmin=220103×60 m3s=3.67×10-3 m3s Length…

Q: At a given instant, the blood pressure in the heart is 1.1 x 104 Pa. If an artery in the brain is…

A: Given Pressure in the heart P=1.1×104 Pa Height of brain h=0.38 m Density of blood ρ=1125kg/m3

Q: Tour tires or an automobile are Inflated to a gauge pressure of 2.3 Pa. Each tire has an area or…

A: Given, pressure, P= 2.3×10⁵ area of tyre, A=0.025m² weight of automobile, W=?Since, automobile is…

Q: The real pressure within a tire or other object containing pressurized stuff would be a combination…

A: Given, gauge pressure on tire = 13.55 psi = 93424 Pa Atmospheric pressure =1.01x105 Pa And Real…

Q: At a given instant, the blood pressure in the heart is 1.1 x 104 Pa. If an artery in the brain is…

Q: The tympanic membrane, or eardrum, is a structure that separates the external and middle parts of…

A: The maximum pressure the membrane can tolerate is the pressure corresponding to the maximum force.…

Concept explainers

Fluid Pressure

The term fluid pressure is coined as, the measurement of the force per unit area of a given surface of a closed container. It is a branch of physics that helps to study the properties of fluid under various conditions of force.

Gauge Pressure

Pressure is the physical force acting per unit area on a body; the applied force is perpendicular to the surface of the object per unit area. The air around us at sea level exerts a pressure (atmospheric pressure) of about 14.7 psi but this doesn’t seem to bother anyone as the bodily fluids are constantly pushing outwards with the same force but if one swims down into the ocean a few feet below the surface one can notice the difference, there is increased pressure on the eardrum, this is due to an increase in hydrostatic pressure.

Topic Video

Question

**Problem Statement:**

At a given instant, the blood pressure in the heart is \(1.7 \times 10^4 \, \text{Pa}\). If an artery in the brain is 0.46 m above the heart, what is the pressure in the artery? Ignore any pressure changes due to blood flow.

**Discussion:**

In this problem, we are asked to determine the pressure within an artery in the brain given the pressure at the heart and the vertical distance between the heart and the brain. We are to disregard any pressure changes attributable to the dynamic flow of blood, implying that we should focus on the hydrostatic pressure difference.

**Key Concepts:**

1. **Pascal's Principle:**
When dealing with fluids at rest (hydrostatics), the pressure change in an incompressible, static fluid is given by the hydrostatic pressure equation:
\[ P_2 = P_1 + \rho g h \]
Where:
- \( P_2 \) is the pressure at the point in question (artery in the brain).
- \( P_1 \) is the initial pressure (pressure in the heart).
- \( \rho \) is the density of the blood (assumed to be 1060 kg/m³).
- \( g \) is the acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \)).
- \( h \) is the height difference (0.46 m in this case).

2. **Hydrostatic Pressure Calculation:**
The difference in heights within a vertical column of fluid results in a difference in pressure between the top and the bottom:
\[ \Delta P = \rho g h \]

**Application to the Problem:**

Given:
- The pressure in the heart, \( P_1 = 1.7 \times 10^4 \, \text{Pa} \)
- The height difference, \( h = 0.46 \, \text{m} \)
- The density of blood, \( \rho = 1060 \, \text{kg/m}^3 \)
- The acceleration due to gravity, \( g = 9.81 \, \text{m/s}^2 \)

We need to find the new pressure \( P_2 \) in the artery located in the brain.

First, calculate the

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1: here I describe the given data

VIEW

Step 2: here we get the final answer

VIEW

Solution

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.

Similar questions

A tall graduated cylinder contains 7 cm of oil (density of 825 kg/m3kg/m3) on top of 20 cm of water (density of 1000 kg/m3kg/m3). The cylinder is open to the air. What is the pressure in the water, 3 cm above the bottom of the cylinder? (in Pa) 1.0323×105 1.0335×105 1.0353×105 1.0294×105 1.0157×105
At a given instant, the blood pressure in the heart is 1.6x104 Pa. If an artery in the brain is 0.45 m above the heart, what is the pressure in the artery? Ignore any pressure changes due to blood flow.
At a given instant, the blood pressure in the heart is 1.4 x 104 Pa. If an artery in the brain is 0.37 m above the heart, what is the pressure in the artery? Ignore any pressure changes due to blood flow.
A 1.50 mL syringe has an inner diameter of 5.50 mm, a needle inner diameter of 0.230 mm, and a plunger pad diameter (where you place your finger) of 1.2 cm. A nurse uses the syringe to inject medicine into a patient whose blood pressure is 140/100. What is the minimum force the nurse needs to apply to the syringe? The nurse empties the syringe in 2.10 s. What is the flow speed of the medicine through the needle?
The blood pressure of an artery is measured at two heights: at the heart and 10 cm above the heart. The mass density of blood is about 1000 kg/m^3 and a typical artery has a diameter of 4 mm. (Use g = 10 m/s^2.) Compared to the pressure at heart height, the pressure 10 cm above is: Group of answer choices 100 P higher 1000 P lower 10 P higher 1000 P higher 100 P lower
A box has a length of 1.3 cm, a width of 6.4 cm, and a height of 3.2 cm. Its mass is 9.8 kg. The box sits at rest on a horizontal floor. What is the pressure of the box on the floor?
Under normal circumstances, the vitreous humor, a jelly-like substance in the main part of the eye, exerts a pressure of up to 24 mmmm of mercury that maintains the shape of the eye. If blockage of the drainage duct for aqueous humor causes this pressure to increase to about 50 mm of mercury, the condition is called glaucoma. What is the increase in the total force (in newtons) on the walls of the eye if the pressure increases from 24 mm to 50 mm of mercury? We can quite accurately model the eye as a sphere 2.2 cm in diameter. Express your answer in newtons.
A fluid with density 1200 kg/m flows through this pipe. As the first location, A, the fluid travels at 7.5 m/s and at the second location, B, the fluid travels at 11 m/s. What is the difference in pressure between the two points? O-1.9 x 10 Pa +3.8 x 103 Pa -2.5 x 104 Pa -3.9 x 10 Pa O +5.0 x 104 Pa
Part A: The human body typically contains 4.9 L of blood of density 1060 kg/m^3 . How many kilograms of blood are in the body? Part B: The average blood pressure is 1.30×104 Pa at the heart. What average force does the blood exert on each square centimeter of the heart? Part C: Red blood cells have a specific gravity of 5.0 and a diameter of about 7.5 μm. If they are spherical in shape (which is not quite true), what is the mass of such a cell?
The pulmonary artery, which connects the heart to the lungs, has an inner radius of 2.60 mm and a length of 8.40 cm. If the drop in pressure between the heart and the lungs is 4.0 hPa. a) What is the average speed of the blood in the pulmonary artery?
The top of a vertical cylinder is sealed with a circular lid. If the cylinder is evacuated, what is the minimum force required to remove the lid from the top of the cylinder? The radius of the cylinder is 6.50 cm. Assume the surrounding air is at a pressure of 1 atm = 1.01 ✕ 105 Pa. Express your answer in units of newtons.
v