At a given instant , the blood pressure in the heart is `1.60 xx 10^(4)` 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 ?

Options

A. `1.6 xx 10^(4) Pa`
B. `9.4 xx 10^(3) Pa`
C. `1.1 xx 10^(4) Pa`
D. `2.1 xx 10^(4) Pa`

Answer

To find the pressure in the artery located 0.45 m above the heart, we can use the hydrostatic pressure formula. The pressure in the artery can be calculated using the following steps:

### Step 1: Identify the known values
- Blood pressure in the heart, \( P_H = 1.60 \times 10^4 \, \text{Pa} \)
- Height difference, \( H = 0.45 \, \text{m} \)
- Density of blood, \( \rho \approx 1060 \, \text{kg/m}^3 \) (standard value for blood)
- Acceleration due to gravity, \( g = 9.81 \, \text{m/s}^2 \)

### Step 2: Write the hydrostatic pressure equation
The pressure at a height \( H \) above a reference point (the heart in this case) is given by:
\[ P_A = P_H - \rho g H \]
where:
- \( P_A \) is the pressure in the artery,
- \( P_H \) is the pressure in the heart,
- \( \rho g H \) is the pressure decrease due to the height difference.

### Step 3: Calculate the pressure decrease due to height
First, we calculate \( \rho g H \):
\[ \rho g H = (1060 \, \text{kg/m}^3)(9.81 \, \text{m/s}^2)(0.45 \, \text{m}) \]
Calculating this gives:
\[ \rho g H = 1060 \times 9.81 \times 0.45 \approx 4677.15 \, \text{Pa} \]

### Step 4: Substitute values into the equation
Now, substitute \( P_H \) and \( \rho g H \) into the equation for \( P_A \):
\[ P_A = 1.60 \times 10^4 \, \text{Pa} - 4677.15 \, \text{Pa} \]

### Step 5: Perform the subtraction
Calculating \( P_A \):
\[ P_A = 16000 - 4677.15 \approx 11322.85 \, \text{Pa} \]

### Step 6: Round the result
Rounding to two significant figures, we get:
\[ P_A \approx 1.13 \times 10^4 \, \text{Pa} \]

### Final Answer
The pressure in the artery is approximately \( 1.13 \times 10^4 \, \text{Pa} \).

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