A pumping machine pumps water at a rate of 60 cc per minute at a pressure of 1.5 atm. The power delivered by the machine is

Options

A. 9 watt
B. 6 watt
C. 9 kW
D. None of these

Answer

To find the power delivered by the pumping machine, we can follow these steps:

### Step 1: Understand the relationship between power, force, and velocity
Power (P) can be expressed as:
\[ P = F \cdot v \]
where \( F \) is the force and \( v \) is the velocity.

### Step 2: Relate force to pressure and area
The force can be expressed in terms of pressure (P) and area (A):
\[ F = P \cdot A \]
Thus, we can rewrite the power equation as:
\[ P = P \cdot A \cdot v \]

### Step 3: Convert the pressure from atm to Pascal
Given the pressure is 1.5 atm, we need to convert it to Pascals. We know:
\[ 1 \text{ atm} = 10^5 \text{ Pa} \]
So,
\[ P = 1.5 \text{ atm} = 1.5 \times 10^5 \text{ Pa} \]

### Step 4: Convert the volume flow rate to standard units
The volume flow rate is given as 60 cc/min. We need to convert this to cubic meters per second:
1 cc = \( 1 \text{ cm}^3 = 10^{-6} \text{ m}^3 \)
1 minute = 60 seconds

Thus,
\[ 60 \text{ cc/min} = 60 \times 10^{-6} \text{ m}^3/\text{min} = \frac{60 \times 10^{-6}}{60} \text{ m}^3/\text{s} = 1 \times 10^{-6} \text{ m}^3/\text{s} \]

### Step 5: Calculate the power
Now we can substitute the values into the power equation:
\[ P = P \cdot A \cdot v \]
Since we don't have the area directly, we can use the volume flow rate (Q) to relate it:
\[ Q = A \cdot v \]
Thus,
\[ A \cdot v = Q \]
Substituting this into the power equation gives:
\[ P = P \cdot Q \]

Now substituting the values:
\[ P = (1.5 \times 10^5 \text{ Pa}) \cdot (1 \times 10^{-6} \text{ m}^3/\text{s}) \]
\[ P = 1.5 \times 10^{-1} \text{ W} = 0.15 \text{ W} \]

### Step 6: Conclusion
The power delivered by the machine is \( 0.15 \text{ W} \). Since this value is not listed among the options, the correct answer is "none of this".

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