Question

A liquid-level system with a cross-sectional area of 3.0 ft² has a valve characteristic given by q = 8√h. Calculate the time constant for this system if the average operating level above the valve is:

(a) 3 ft
(b) 9 ft

Answer 1

To calculate the time constant for the liquid-level system, use the given valve characteristic equation to determine the initial and final flow rates for different average operating levels. Then, use the formula τ = (q2 - q1) / Δh to calculate the time constant.

Step-by-step explanation:

To calculate the time constant for the liquid-level system, we first need to determine the flow rate (q) in terms of the liquid level (h). The given valve characteristic is q = 8√h. The time constant (τ) is equal to the ratio of the change in liquid level (Δh) to the change in flow rate (Δq). In this case, Δq can be calculated by subtracting the initial flow rate (q1) from the final flow rate (q2), which can be determined using the given valve characteristic equation.

For part (a) where the average operating level is 3 ft, we can substitute h = 3 into the valve characteristic equation to find the initial flow rate (q1). Then, we can substitute h = 0 to find the final flow rate (q2). Once we have q1 and q2, we can calculate the time constant using the formula τ = (q2 - q1) / Δh.

Similarly, for part (b) where the average operating level is 9 ft, we can follow the same steps to find the time constant.