Chapter 11, Problem 11.32P

To determine

(a)

The diameter of the impeller.

Answer to Problem 11.32P

The required value of the diameter is $15.5in$

Explanation of Solution

Given Information:

Given data from problem $11.31$.

$Temperature\left(T\right)={20}^{o}C$

$N_p=1200r/\min$

Formula used:

$H_o=0.6U^2/g\pm 6\%$

$U=\omega D/2$

$\omega =2\pi n/60$

Calculation:

As in the last problem, we solved it by using ratio.

We know that for a wide range of centrifugal pumps, the shut off head $H_o=0.6U^2/g\pm 6\%$ Here U is the impeller blade tip velocity $U=\omega D/2$ . We would use this to estimate with the shut off head and speed of the pump in prob. 11.31:

$\omega =2\pi \left(1200rpm\right)/60$

$\Rightarrow 126rad/s$

$H_o=123ft=0.6\left[{\left(126D/2\right)}^2/32.2ft/s^2\right]$

$D=1.29ft=15.5in$.

To determine

(b)

BEP parameters.

Answer to Problem 11.32P

The required value of the BEP parameters are:

$C_Q{}^{*}=$

$0.103$

$C_H{}^{*}=$

$3.9$

$C_P{}^{*}=$

$0.47$

Explanation of Solution

Given information:

$Temperature\left(T\right)={20}^{o}C$

$N_p=1200r/\min$

Formula used:

$C_Q{}^{*}=\frac{Q_1}{n_1{D}_1{}^3}$ = $\frac{Q_2}{n_2{D}_2{}^3}$

$C_P{}^{*}=\frac{P_1}{\rho n_1{}^3{D}_1{}^5}=\frac{P_2}{\rho n_2{}^3{D}_2{}^5}$

Calculation:

Since we know the diameter $D=1.29ft$ and speed $n=1200/60$, we can calculate;

$n=1200/60$

$\Rightarrow 20r/s$

$C_Q{}^{*}=\frac{\left(2000/448.8\right)f{t}^3/s}{\left(20r/s\right){\left(1.29ft\right)}^3}$

$\Rightarrow 0.103$

Again, $C_H{}^{*}=\frac{\left(32.2ft/s^2\right)81ft}{{\left(20r/s\right)}^2{\left(1.29ft\right)}^3}$

$\Rightarrow 3.9$

$C_P{}^{*}=\frac{\left(48\right)\left(550ft\cdot lbf/s\right)}{\left(1.94slug/f{t}^3\right){\left(20r/s\right)}^3{\left(1.29ft\right)}^5}$

$\Rightarrow 0.47ans\left(b\right)$.

To determine

(a)

Speed of the pump for given parameters.

Answer to Problem 11.32P

The required value of the speed is $2230r/\min$

Explanation of Solution

Given Information:

$Temperature\left(T\right)={20}^{o}C$

$\begin{array}{l}{N}_p=1200r/\min \\ BEPhead\left(h\right)=280ft\end{array}$

Formula used:

$C_H*=\frac{g{H}_1}{n_1{}^2{D}_1{}^2}=\frac{g{H}_2}{n_2{}^2{D}_2{}^2}$

Calculation:

Since we know the head, i.e. $280ft$ ;

$C_H{}^{*}=3.9=\frac{\left(32.2ft/s^2\right)\left(280ft\right)}{n^2{\left(1.29ft\right)}^2}$

$n=37r/s$

$\Rightarrow 2230r/\min$.