Question 10.9: Compute the expansion tank volume for a chilled water system......

A bladder type would be the best choice; however, calculations will be made for both types. Equation 10-33 will give the volume of the free liquid–air interface type tank where ν_{2}  =  0.01613  ft^{3}/lbm  and  ν_{1}  =  0.01602  ft^{3}/lbm from Table A-1a:

V_{T}  =  \frac{V_{\text{w}} \left[\left\lgroup \frac{\text{v}_{2}}{\text{v}_{1}}  –  1\right\rgroup \right]  –  3\alpha  Δt}{\frac{P_{a}}{P_{1}}  –  \frac{P_{a}}{P_{2}}}                                  (10-33)

V_{TF}  =  \frac{2000(\frac{0.01613}{0.01602}  –  1)  –  3(6.5  ×  10^{-6})  (55)}{(\frac{14.696}{24.696}  –  \frac{14.696}{49.696})}

V_{TF}  =  38.7  gal  =  5.2  ft^{3}

Equation 10-34 will give the volume of the bladder-type tank:

V_{T}  =  \frac{V_{\text{w}} \left[\left\lgroup \frac{\text{v}_{2}}{\text{v}_{1}}  –  1\right\rgroup \right]  –  3\alpha  Δt}{1  –  \frac{P_{1}}{P_{2}}}                                  (10-34)

V_{TF}  =  \frac{2000\left[(\frac{0.01613}{0.01602}  –  1)  –  3(6.5  ×  10^{-6})  (55)\right]}{1  –  \frac{14.696}{49.696}}

V_{TF}  =  23.0  gal  =  3.1  ft^{3}

Note that the volume of the bladder-type tank is less than the free-surface type. This is an advantage in large systems.