Question

Water (ρ = 1000 kg/m³) flows through a venturimeter with inlet diameter 80 mm and throat diameter 40 mm. The inlet and throat gauge pressures are measured to be 400 kPa and 130 kPa respectively. Assuming the venturimeter to be horizontal and neglecting friction, the inlet velocity (in m/s) is ________.

Answer 1

Explanation:

Using Bernoulli’s equation: 

 \(\frac{{{P_1}}}{{{ρ _g}}} + \frac{{v_1^2}}{{2g}} + {z_1} = \frac{{{p_2}}}{{ρ g}} + \frac{{v_2^2}}{{2g}} + {z_2}\)

Given that

→ P₁ = 400000 Pa, P₂ = 130000 Pa,   Z₁ = Z₂ and ρ = 1000

_{Apply Continuity Equation:}

 A1V1 = A₂V₂

\(\frac{\pi }{4}{(80)^2}{V_1} = \frac{\pi }{4}{(40)^2}{V_2}\)

_V2 = 4V₁

\({\frac{{{400000} }}{{ρ g}}} + \frac{{V_1^2}}{{2g}} = { {\frac{{130}000}{{ρ g}}}} + {{\frac{{(4{V_1})^2}}{{2g}}}} \)

\(400 + \frac{{V_1^2}}{2} = 130 + \frac{{16V_1^2}}{2}\)

\(\frac{{15V_1^2}}{2} = 270\;\)

\(V_1^2 = 36\)

V₁ = 6 m/s