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Chapter 8: Problem 195

A venturi meter with a 3 -in. -diameter throat is placed in a 6 -in.-diameter line carrying water at \(75^{\circ} \mathrm{F}\), The pressure drop between the upstream tap and the venturi throat is 12 in. of mercury. Compute the rate of flow.

Short Answer

Expert verified
The flow rate \(Q\) can be calculated by replacing the known parameters in the formula \(Q = Cd \times \frac{{\pi D虏 d虏 \sqrt{2gh}}}{{\sqrt{{(D虏 - d虏)}}}}\), which will give the flow rate in m鲁/s.

Step by step solution

01

Understand and calculate necessary parameters

Firstly, the key parameters to understand are the diameters of the pipe (\(D\)) and the Venturi meter (\(d\)), and the difference in pressure between the pipe and the throat (\(h\)), which are given as 6 inches, 3 inches and 12 inches of mercury respectively. Next, we need to convert these measurements into appropriate units. A useful information is that 1 inch of mercury equals 13,595.1 kg/m鲁. Thus, \(h = 12 \times 13,595.1\) kg/m鲁. Also, convert inches into meters, given 1 inch = 0.0254 m. Therefore, \(D= 6 \times 0.0254\) m and \(d = 3 \times 0.0254\) m.
02

Determine the coefficient of discharge (Cd)

The coefficient of discharge can vary with the meter design, but in the case of a well-designed Venturi meter, it can be taken as approximately 0.98.
03

Calculate the flow rate using the Venturi equation

The Venturi meter equation is given by \(Q = Cd \times \frac{{\pi D虏 d虏 \sqrt{2gh}}}{{\sqrt{{(D虏 - d虏)}}}}\), where \(Q\) is the flow rate, \(D\) and \(d\) are the diameters of the pipe and the venturi meter throat respectively, \(h\) is the height of fluid column, \(g\) is the acceleration due to gravity (9.81 m/s虏) and \(Cd\) is the discharge coefficient. Replacing the known quantities in this formula will give the flow rate \(Q\) in m鲁/s.

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