Glycerine flows steadily through a horizontal tube of length 1.5m and radius 1.0 cm. if the amount of glycerine collected per second at one end is `4.0 xx 10^(-3) kg s^(-1)`, what is the pressuer difference between the two ends of the tube? (density of glycerine = `1.3xx10^(3)kgm^(-3)` and viscosity of glycerine =`0.83Ns m^(-2)`).

Explanation

To find the pressure difference between the two ends of the tube through which glycerine flows, we can use the Hagen-Poiseuille equation, which relates the pressure difference to the flow rate, viscosity, length of the tube, and radius of the tube.

### Step-by-Step Solution:

1. **Identify Given Values:**
- Length of the tube, \( L = 1.5 \, \text{m} \)
- Radius of the tube, \( r = 1.0 \, \text{cm} = 0.01 \, \text{m} \)
- Mass flow rate, \( \dot{m} = 4.0 \times 10^{-3} \, \text{kg/s} \)
...