Short answer
Yes. In the Hanafi school, any discharge that comes out of the vagina breaks wudu, including normal clear or white discharge. The four schools agree on this. If it flows almost constantly, the rules for an excused person (ma'dhur) apply.
Discharge that leaves the front passage breaks wudu, whatever its colour. Imam Abu Hanifa held that ordinary discharge from inside is pure, so it does not have to be washed from clothes, while his two students held it impure; washing it off is the safer choice. Discharge that is mixed with blood or from an infection is impure.
The four schools agree on this.
Explanation
Anything that comes out of the front or back passage breaks wudu (ablution), and vaginal discharge is no exception. The four schools agree on this. It applies to white, clear or yellowish discharge, and to the wetness some women notice with arousal (which is madhy, see precum and ghusl).
When does it count as "coming out"? In the Hanafi school, wudu breaks when the discharge reaches the outer part of the private area, the part you wash in istinja. Moisture you feel inside that has not come out does not break it.
Is it impure on your clothes? Imam Abu Hanifa held that ordinary moisture from inside the vagina is pure. His students Abu Yusuf and Muhammad held it impure. Many Hanafi muftis follow the Imam's view for normal discharge, so a woman need not change her underwear for every prayer, while noting that washing it is better. Discharge with blood, pus or a bad smell from infection is impure.
If discharge flows so often that you cannot keep wudu long enough to pray a fard prayer within its time, you are ma'dhur (excused): make wudu once in each prayer time and pray with it. See praying with a continuous condition. A panty liner you change before prayer can make life easier. Because cases differ, ask a qualified mufti about your own situation.
Ask a mufti about your own case. This answer explains the general ruling. When the details of your situation matter, as they do here, ask a qualified mufti and give them the full facts. Where to ask a scholar.
The evidence
Quran, Surah Al-Maaida 5:6
يَٰٓأَيُّهَا ٱلَّذِينَ ءَامَنُوٓا۟ إِذَا قُمْتُمْ إِلَى ٱلصَّلَوٰةِ فَٱغْسِلُوا۟ وُجُوهَكُمْ وَأَيْدِيَكُمْ إِلَى ٱلْمَرَافِقِ وَٱمْسَحُوا۟ بِرُءُوسِكُمْ وَأَرْجُلَكُمْ إِلَى ٱلْكَعْبَيْنِ ۚ وَإِن كُنتُمْ جُنُبًۭا فَٱطَّهَّرُوا۟ ۚ وَإِن كُنتُم مَّرْضَىٰٓ أَوْ عَلَىٰ سَفَرٍ أَوْ جَآءَ أَحَدٌۭ مِّنكُم مِّنَ ٱلْغَآئِطِ أَوْ لَٰمَسْتُمُ ٱلنِّسَآءَ فَلَمْ تَجِدُوا۟ مَآءًۭ فَتَيَمَّمُوا۟ صَعِيدًۭا طَيِّبًۭا فَٱمْسَحُوا۟ بِوُجُوهِكُمْ وَأَيْدِيكُم مِّنْهُ ۚ مَا يُرِيدُ ٱللَّهُ لِيَجْعَلَ عَلَيْكُم مِّنْ حَرَجٍۢ وَلَٰكِن يُرِيدُ لِيُطَهِّرَكُمْ وَلِيُتِمَّ نِعْمَتَهُۥ عَلَيْكُمْ لَعَلَّكُمْ تَشْكُرُونَ ﴿٦﴾
O you who have believed, when you rise to [perform] prayer, wash your faces and your forearms to the elbows and wipe over your heads and wash your feet to the ankles. And if you are in a state of janabah, then purify yourselves. But if you are ill or on a journey or one of you comes from the place of relieving himself or you have contacted women and do not find water, then seek clean earth and wipe over your faces and hands with it. Allah does not intend to make difficulty for you, but He intends to purify you and complete His favor upon you that you may be grateful.
Shows that what leaves the private passages calls for fresh purification before prayer.
Sahih al-Bukhari 135
Sahih... لا تقبل صلاة من احدث حتى يتوضا ...
"The prayer of someone who has broken his wudu is not accepted until he makes wudu."
Prayer needs wudu again after anything that breaks it, including what leaves the front passage.
Where the ruling is recorded
- Radd al-Muhtar (Ibn Abidin), Kitab al-Taharah, nawaqid al-wudu and chapter on impurities. Discharge breaks wudu; the difference between Abu Hanifa and his students on its purity.
- al-Fatawa al-Hindiyya, Kitab al-Taharah, chapter on what breaks wudu. What leaves the front passage breaks wudu.
- al-Majmu' (Nawawi), Kitab al-Taharah, chapter on impurities. The Shafi'i discussion of the moisture of the private part.
This answer is pending review by the scholars on our team. Quran translation by Sahih International. Hadith Arabic from the standard editions of the six books and the Muwatta, with gradings as recorded there; the English is our own rendering. Spotted a mistake? Tell us.