Does a Shower Count as Wudu?
Question

Is it correct to pray without wudu immediately after coming from a normal bath?
Praise be to Allah.Wudu before ghusl
It is recommended for a Muslim to do wudu before ghusl following the example of the Prophet (peace and blessings of Allah be upon him). 
If ghusl is done in cases of major impurity such as janabah (impurity following sexual activity) and menstruation, and the person washes his entire body with water, as well as rinsing out the mouth and nose, then it is sufficient and there is no need to do wudu . The Prophet (peace and blessings of Allah be upon him) did not do wudu after doing ghusl. 
Does a shower count as wudu?
But if the “ghusl” is done to cool down or to clean oneself, then it does not take the place of wudu. 
Shaykh Muhammad ibn Salih al-‘Uthaymin (may Allah have mercy on him) said: Does ghusl following janabah take the place of wudu? 
He replied: 
“If a person is in a state of janabah and he does ghusl, then that is sufficient and he does not need to do wudu, because Allah says (interpretation of the meaning): 
“If you are in a state of Janabah (i.e. after a sexual discharge), purify yourselves (bathe your whole body)” [al-Maidah 5:6]
There is no need to repeat wudu after doing ghusl . But if one of the things that break wudu takes place, and he breaks his wudu after doing ghusl, then he must do wudu. But if he does not break his wudu, then his doing ghusl from janabah takes the place of wudu, whether he did wudu before doing ghusl or not. But it is essential to pay attention to rinsing the mouth and nose, because doing so is essential in both wudu and ghusl.” (Majmu’ Fatawa al-Shaykh Ibn ‘Uthaymin, 11/question no. 180) 
Shaykh Muhammad ibn Salih al-‘Uthaymin (may Allah have mercy on him) was also asked: Does ghusl that is not prescribed or required according to Shari`ah take the place of wudu? 
He replied: 
“Ghusl that is not prescribed or required according to Shari`ah does not take the place of wudu, because it is not an act of worship.” (Majmu’ Fatawa al-Shaykh Ibn ‘Uthaymin, 11/question no. 181) 
He (may Allah have mercy on him) was also asked: Does taking a bath take the place of wudu? 
He replied: 
“If a person takes a bath because of janabah, then it takes the place of wudu, because Allah says (interpretation of the meaning): 
“If you are in a state of Janaba (i.e. after a sexual discharge), purify yourselves (bathe your whole body)” [al-Maidah 5:6]
If a person is junub and he immerses himself in a bathtub or river or the like, intending thereby to cleanse himself of janabah, and he rinses his mouth and nose, then he purifies himself from both minor and major impurity, because Allah, may He be exalted, only enjoined us to purify ourselves from janabah, i.e., we should ensure that water reaches all parts of the body when doing ghusl. But it is better for the person who is doing ghusl to do wudu first, because the Prophet (peace and blessings of Allah be upon him) used to wash his private parts after washing his hands, then he would do wudu as for prayer, then he would pour water over his head, and when he thought that it had reached the skin, he poured water over his head three times, then he would wash the rest of his body. 
But if a person takes a bath to clean himself or to cool himself down, then this does not take the place of wudu, because that is not an act of worship, rather it is just an ordinary action, although Islam prescribes cleanliness. 
Whatever the case, if the bath is taken to cool down or get clean, then it does not take the place of wudu.” (Majmu’ Fatawa al-Shaykh Ibn ‘Uthaymin, 11/question no. 182) 
And Allah knows best.