60000 Pa + 1000 kg/m3 / 2 ( (2.547 m/s) ^2 - (10.20 m/s) ^2)

Let's break down and solve the given expression step by step:

Expression:

\[
60000 \, \text{Pa} + \frac{1000 \, \text{kg/m}^3}{2} \left( (2.547 \, \text{m/s})^2 - (10.20 \, \text{m/s})^2 \right)
\]

### Step 1: Evaluate the squares
We first calculate the squares of the velocities \(2.547 \, \text{m/s}\) and \(10.20 \, \text{m/s}\):

\[
(2.547 \, \text{m/s})^2 = 6.484809 \, \text{m}^2/\text{s}^2
\]
\[
(10.20 \, \text{m/s})^2 = 104.0400 \, \text{m}^2/\text{s}^2
\]

### Step 2: Subtract the results
Now, subtract the results of the squared terms:

\[
6.484809 \, \text{m}^2/\text{s}^2 - 104.0400 \, \text{m}^2/\text{s}^2 = -97.555191 \, \text{m}^2/\text{s}^2
\]

### Step 3: Multiply by the mass density and divide by 2
Next, apply the mass density \(1000 \, \text{kg/m}^3\) and divide by 2:

\[
\frac{1000 \, \text{kg/m}^3}{2} \times (-97.555191 \, \text{m}^2/\text{s}^2) = -48777.5955 \, \text{Pa}
\]

### Step 4: Add to the pressure term
Finally, add the result to the initial pressure \(60000 \, \text{Pa}\):

\[
60000 \, \text{Pa} + (-48777.5955 \, \text{Pa}) = 11222.4045 \, \text{Pa}
\]

### Final Answer:
\[
11222.4045 \, \text{Pa} \approx 11222.40 \, \text{Pa}
\]

Let me know if you'd like further details or have any questions!

### Relative Questions:
1. What are the applications of such fluid dynamic equations?
2. How does velocity influence pressure in fluid systems?
3. Can you derive Bernoulli's equation using these parameters?
4. How do you convert pressure units from Pascals to other units like atm or mmHg?
5. Why is the density of a fluid a critical factor in pressure calculations?

### Tip:
Always ensure your units are consistent when performing calculations in physics or engineering problems, especially in fluid dynamics.

Solve a fluid dynamics problem involving pressure and velocity difference with step-by-step calculations. This problem uses Bernoulli's principle and involves calculating kinetic energy terms in fluid motion. Suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation