# 013 Review Problem - Volume of water inside the Venturi meter

**Problem 13**

The accompanying figure represents the longitudinal view of a Venturi meter, a device designed to measure the flow of water in pipes. If the throat of the of the meter is 6 in. long and has an inside diameter of 4 in., find the volume of water in the meter which is used in 12-in. pipe line if the altitudes of the tapering parts are in the ratio 1:3 and the smaller altitude measures 12 in.

**Solution 13**

$L = 36 ~ \text{in.}$

$V_1 = \text{Frustum of a right circular cone}$

$V_1 = \frac{1}{3}\pi h(R^2 + r^2 + Rr)$

$V_1 = \frac{1}{3}\pi (12)[ \, 6^2 + 2^2 + 6(2) \, ]$

$V_1 = 208\pi ~ \text{in.}^3$

$V_2 = \text{Right circular cylinder}$

$V_2 = pi r^2 h$

$V_2 = \pi (2^2)(6)$

$V_2 = 24\pi ~ \text{in.}^3$

$V_3 = \text{Frustum of a right circular cone}$

$V_3 = \frac{1}{3}\pi L(r^2 + R^2 + rR)$

$V_3 = \frac{1}{3}\pi(36) [ \, 2^2 + 6^2 + 2(6) \, ]$

$V_3 = 624\pi ~ \text{in.}^3$

Total volume

$V = V_1 + V_2 + V_3$

$V = 208\pi + 24\pi + 624\pi$

$V = 856\pi ~ \text{in.}^3$

$V = 2689.2 ~ \text{in.}^3$ *answer*

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