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### ? Formula for Mass Flow Rate
The mass flow rate $\dot{m}$ is given by:

\[
\dot{m} = \rho \cdot A \

Question

Act like a helpful tutor and exlain me :
Great question! Let’s work this out step by step ?

### ? Formula for Mass Flow Rate
The mass flow rate $\dot{m}$ is given by:

$$
\dot{m} = \rho \cdot A \cdot V
$$

Where:  
- $\rho$ = density of fluid (kg/m³)  
- $A$ = cross-sectional area of pipe (m²)  
- $V$ = velocity of fluid (m/s)

---

### ? Substitution
- $\rho = 900 \, \text{kg/m}^3$  
- $A = 0.05 \, \text{m}^2$  
- $V = 1.6 \, \text{m/s}$

$$
\dot{m} = 900 \cdot 0.05 \cdot 1.6
$$

---

### ? Calculation
$$
\dot{m} = 900 \cdot 0.08 = 72 \, \text{kg/s}
$$

---

✅ **Final Answer:**  
The **mass flow rate** of the liquid is:

$$
\boxed{72 \, \text{kg/s}}
$$

---

Would you like me to also show you how to calculate the **volumetric flow rate** (which is often paired with mass flow rate in fluid mechanics problems)?

VIPSolutions · Accepted Answer

# How to Calculate Volumetric Flow Rate

Yes! Let’s walk through how to find the **volumetric flow rate** step by step.

---

## 1. Volumetric Flow Rate Formula

The **volumetric flow rate** $ Q $ is given by:

$$
Q = A \cdot V
$$

Where:  
- $ Q $ = volumetric flow rate (in m³/s)  
- $ A $ = cross-sectional area of pipe (in m²)  
- $ V $ = velocity of the fluid (in m/s)

---

## 2. Substituting Your Values

Given:  
- $ A = .05 \, \text{m}^2 $  
- $ V = 1.6 \, \text{m/s} $

Plug in the values:

$$
Q = .05 \cdot 1.6
$$

---

## 3. Calculation

$$
Q = .08 \, \text{m}^3/\text{s}
$$

---

## 4. Final Answer

$$
\boxed{.08 \, \text{m}^3/\text{s}}
$$

---

## 5. Relationship Between Mass and Volumetric Flow Rate

Recall from before:

$$
\dot{m} = \rho Q
$$

Where $\rho$ is the density. Using your previous answers:

$$
\dot{m} = 900 \times .08 = 72 \, \text{kg/s}
$$

This matches your original calculation.

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**Summary Table**

| Quantity                | Formula                  | Value      |
|-------------------------|-------------------------|------------|
| Mass flow rate ($\dot{m}$)    | $\rho A V$ or $\rho Q$ | $72\,\text{kg/s}$ |
| Volumetric flow rate ($Q$) | $A V$                    | $.08\,\text{m}^3/\text{s}$ |

---

**Let me know if you want more details or examples!**

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