Bernoulli's Principle

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Water flows through a horizontal pipe. The area of cross-section at one place is 10 cm^2 and velocity is 1 m/s. At another place, the area is 5 cm^2. The pressure difference between the two places is (density = 1000 kg/m^3):

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1. **Equation of Continuity**: $A_1 v_1 = A_2 v_2$.
   $$10 	imes 1 = 5 	imes v_2 \implies v_2 = 2	ext{ m/s}$$
2. **Bernoulli's Equation (Horizontal)**: $P_1 + \frac{1}{2}ho v_1^2 = P_2 + \frac{1}{2}ho v_2^2$.
3. **Pressure Difference**: $P_1 - P_2 = \frac{1}{2}ho(v_2^2 - v_1^2)$.
4. **Calculation**: $P_1 - P_2 = \frac{1}{2}(1000)(2^2 - 1^2) = 500(3) = 1500	ext{ Pa}$.

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Bernoulli's Principle

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