Concept explainers
(a)
To determine the maximum height that the water will reach in the tank.
Explanation of Solution
The diameter of the tank is
The following figure shows the schematic diagram of water tank system.
Figure-(1)
Write the expression for Bernoulli theorem between the point
Here, the pressure at point
Substitute
Write the expression for the mass flow rate at the point
Here, the area of the orifice is
Write the expression for the area of the orifice.
Here, the diameter of the orifice is
Substitute
Square on both sides in Equation (IV).
Substitute
Substitute
The maximum height reached by the water of the tank is
(b)
The relation between water height as a function of time.
Explanation of Solution
Write the expression for the principle of conservation of mass for the control volume undergoing a change during period
Here, the mass flow rate of orifice is
Write the expression for the mass flow rate of control volume.
Substitute
Substitute
Write the general expression for
Differentiate Equation (X).
Substitute
Write the expression for the dissolve of fraction.
Dissolve the fraction in Equation (X).
Equate the coefficients of
Substitute
Substitute
Substitute
Integrate Equation (XII) on both sides.
Substitute
Substitute
The relation between the time and the height is
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- Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning