Ethanol of density `rho = 791 kg//m^(3)` flows smoothly through a horizontal pipe that tapers (as in Fig ) in cross-sectional area from `A_(1) = 1.20 xx 10^(-3) m^(2)` to `A_(2) = A_(1)//2` . The pressure difference between the wide and narrow sectional of pipe is 4120 Pa. What is the volume flow rate `R_(v)` of the ethanol ?

Explanation

To solve the problem of finding the volume flow rate \( R_v \) of ethanol flowing through a tapering pipe, we can follow these steps:

### Step 1: Identify Given Data
- Density of ethanol, \( \rho = 791 \, \text{kg/m}^3 \)
- Cross-sectional area at the wider section, \( A_1 = 1.20 \times 10^{-3} \, \text{m}^2 \)
- Cross-sectional area at the narrower section, \( A_2 = \frac{A_1}{2} = \frac{1.20 \times 10^{-3}}{2} = 0.60 \times 10^{-3} \, \text{m}^2 \)
- Pressure difference, \( P_1 - P_2 = 4120 \, \text{Pa} \)

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