What is the skin-friction coefficient for a turbulent boundary layer on a flat plate, when [latex]M_e=2.5, \operatorname{Re}_x=6.142 \times 10^6[/latex], and [latex]T_w=3.0 T_e[/latex] ?

For these calculations, [latex]F_c=2.056(\text { see Table 8.4) }[/latex] and [latex]F_{\mathrm{Re}}=0.1729(\text { see Table 8.5) }[/latex] Thus, [latex]\mathrm{Re}_x F_{\mathrm{Re}}=1.062 \times 10^6[/latex] Using Table 8.6, we obtain [latex]F_c C_f=0.0035[/latex] so that [latex]C_f=1.70 \times 10^{-3}[/latex]

Question 8.5: What is the skin-friction coefficient for a turbulent bounda......

Aerodynamics for Engineers [1362363]

What is the skin-friction coefficient for a turbulent boundary layer on a flat plate, when $M_e=2.5, \operatorname{Re}_x=6.142 \times 10^6$ , and $T_w=3.0 T_e$ ?

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For these calculations,

$F_c=2.056(\text { see Table 8.4) }$

and

$F_{\mathrm{Re}}=0.1729(\text { see Table 8.5) }$

Thus,

$\mathrm{Re}_x F_{\mathrm{Re}}=1.062 \times 10^6$

Using Table 8.6, we obtain

$F_c C_f=0.0035$

so that

$C_f=1.70 \times 10^{-3}$

\text { TABLE 8.4 Values of } F_{\mathrm{c}} \text { as a Function of } M_{\mathrm{e}} \text { and } T_w / T_{\mathrm{e}}

$M_e$
$\frac{T_w}{T_{\mathrm{e}}}$	0.0	1.0	2.0	3.0	4.0	5.0	6.0
0.05	0.3743	0.4036	0.4884	0.6222	0.7999	1.0184	1.2759
0.10	0.4331	0.4625	0.5477	0.6829	0.8628	1.0842	1.3451
0.20	0.5236	0.5530	0.6388	0.7756	0.9584	1.1836	1.4491
0.30	0.5989	0.6283	0.7145	0.8523	1.0370	1.2649	1.5337
0.40	0.6662	0.6957	0.7821	0.9208	1.1069	1.3370	1.6083
0.50	0.7286	0.7580	0.8446	0.9839	1.1713	1.4031	1.6767
0.60	0.7873	0.8168	0.9036	1.0434	1.2318	1.4651	1.7405
0.80	0.8972	0.9267	1.0137	1.1544	1.3445	1.5802	1.8589
1.00	1.0000	1.0295	1.1167	1.2581	1.4494	1.6871	1.9684
2.00	1.4571	1.4867	1.5744	1.7176	1.9130	2.1572	2.4472
3.00	1.8660	1.8956	1.9836	2.1278	2.3254	2.5733	2.8687
4.00	2.2500	2.2796	2.3678	2.5126	2.7117	2.9621	3.2611
5.00	2.6180	2.6477	2.7359	2.8812	3.0813	3.3336	3.6355
6.00	2.9747	3.0044	3.0927	3.2384	3.4393	3.6930	3.9971
8.00	3.6642	3.6938	3.7823	3.9284	4.1305	4.3863	4.6937
10.00	4.3311	4.3608	4.4493	4.5958	4.7986	5.0559	5.3657

Source: Spalding and Chi (1964).

\text { TABLE 8.5 Values of } F_{\mathrm{Re}} \text { as a Function of } M_{\mathrm{e}} \text { and } T_w / T_{\mathrm{e}}

$M_e$
$\frac{T_w}{T_{\mathrm{e}}}$	0.0	1.0	2.0	3.0	4.0	5.0	6.0
0.05	221.0540	232.6437	256.5708	278.2309	292.7413	300.8139	304.3061
0.10	68.9263	73.0824	82.3611	91.2557	97.6992	101.7158	103.9093
0.20	20.4777	22.0029	25.4203	28.9242	31.6618	33.5409	34.7210
0.30	9.8486	10.6532	12.5022	14.4793	16.0970	17.2649	18.0465
0.40	5.7938	6.2960	7.4742	8.7703	9.8686	10.6889	11.2618
0.50	3.8127	4.1588	4.9812	5.9072	6.7120	7.3304	7.7745
0.60	2.6969	2.9499	3.5588	4.2576	4.8783	5.3658	5.7246
0.80	1.5487	1.7015	2.0759	2.5183	2.9247	3.2556	3.5076
1.00	1.0000	1.1023	1.3562	1.6631	1.9526	2.1946	2.3840
2.00	0.2471	0.2748	0.3463	0.4385	0.5326	0.6178	0.6903
3.00	0.1061	0.1185	0.1512	0.1947	0.2410	0.2849	0.3239
4.00	0.0576	0.0645	0.0829	0.1079	0.1352	0.1620	0.1865
5.00	0.0356	0.0400	0.0516	0.0677	0.0856	0.1036	0.1204
6.00	0.0240	0.0269	0.0349	0.0460	0.0586	0.0715	0.0834
8.00	0.0127	0.0143	0.0187	0.0248	0.0320	0.0394	0.0466
10.00	0.0078	0.0087	0.0114	0.0153	0.0198	0.0246	0.0294

\text { TABLE 8.6 Values of } F_c C_f \text { as a Function of } F_{\mathrm{Re}} \operatorname{Re}_{\mathrm{x}}

$F_c C_f$	$F_{\mathrm{Re}} \mathrm{Re}_{\mathrm{x}}$	$F_c C_f$	$F_{\mathrm{Re}} \mathrm{Re}_{\mathrm{x}}$
0.0010	$5.758 \times 10^{10}$	0.0055	$8.697 \times 10^4$
0.0015	$4.610 \times 10^8$	0.0060	$5.679 \times 10^4$
0.0020	$4.651 \times 10^7$	0.0065	$3.901 \times 10^4$
0.0025	$9.340 \times 10^6$	0.0070	$2.796 \times 10^4$
0.0030	$2.778 \times 10^6$	0.0075	$2.078 \times 10^4$
0.0035	$1.062 \times 10^6$	0.0080	$1.592 \times 10^4$
0.0040	$4.828 \times 10^5$	0.0085	$1.251 \times 10^4$
0.0045	$2.492 \times 10^5$	0.0090	$1.006 \times 10^4$
0.0050	$1.417 \times 10^5$